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Spin-charge separation in the single-hole-doped Mott antiferromagnet Z.Y.Weng,1V.N.Muthukumar,2D.N.Sheng,1,3and C.S.Ting1
1Texas Center for Superconductivity,University of Houston,Houston,Texas77204-5506
2Joseph Henry Laboratories of Physics,Princeton University,Princeton,New Jersey08544 3Department of Physics and Astronomy,California State University,Northridge,California91330
?Received23August2000;published16January2001?
The motion of a single hole in a Mott antiferromagnet is investigated based on the t-J model.An exact expression of the energy spectrum is obtained,in which the irreparable phase string effect?Phys.Rev.Lett.77, 5102?1996??is explicitly present.By identifying the phase string effect with spin back?ow,we point out that spin-charge separation must exist in such a system:the doped hole has to decay into a neutral spinon and a spinless holon,together with the phase string.We show that while the spinon remains coherent,the holon motion is deterred by the phase string,resulting in its localization in space.We calculate the electron spectral function which explains the line shape of the spectral function as well as the‘‘quasiparticle’’spectrum observed in angle-resolved photoemission experiments.Other analytic and numerical approaches are discussed based on the present framework.
DOI:10.1103/PhysRevB.63.075102PACS number?s?:71.27.?a,74.20.Mn,74.72.?h
I.INTRODUCTION
Since the discovery of high-T c superconductivity,there has been much effort to elucidate the properties of doped Mott insulators.In this context,the speci?c case of one hole in a Mott insulating antiferromagnet?half-?lled band?has been the subject of extensive theoretical and experimental investigation.These studies address the basic question of whether the motion of a hole in the antiferromagnet can pos-sibly be described within a quasiparticle approach.Photo-emission spectroscopy provides valuable information that can help resolve this issue.Experimental results from angle-resolved photoemission spectroscopy?ARPES?are now available for Sr2CuO2Cl2as well as for Ca2CuO2Cl2.1–5 Both these materials are Mott insulators and are parent com-pounds of the high-T c cuprates.The results from ARPES can be summarized as follows:?i?the spectral features observed are not sharp at all.Quite to the contrary,an intrinsic broad feature extending to energies of the order of1.5eV before merging into the main valence band is seen.This is to be contrasted with sharp spectral features that one expects in a quasiparticle scenario;?ii?the observed dispersion is isotro-pic around k0?(?/2,?/2);?iii?the measurements of Ron-ning et al.3reveal the presence of a so-called remnant Fermi surface of the momentum structure in the energy-integrated spectral function.
The broad spectral features seen in ARPES strongly sug-gest the breakdown of the quasiparticle picture.Based on such considerations,Laughlin6conjectured the failure of quasiparticle theory in these materials,and further proposed that the observed isotropic dispersion has its origins in an underlying spinon spectrum.This picture envisages spin-charge separation with the scale of the observed dispersion determined by the superexchange J.
An entirely different picture is presented by the self-consistent Born approximation?SCBA?approach.7–10 Though this scheme is based on the t-J model,it depicts a spin-polaron picture for the single hole case where the doped hole behaves not very different from a quasiparticle in the Landau-Fermi liquid theory.The SCBA results have also been supported by exact numerical calculations on?nite lattices11up to32sites12as well as variational calculations on larger lattices.13Here,the consistency among different numerical methods mostly concerns the spectrum?k,usually de?ned as the minimum energy for a given momentum k. The spectrum is anisotropic around the‘‘Fermi points’’k0?(??/2,??/2)in all these calculations.It is called a‘‘qua-siparticle’’spectrum since a sharp peak in the spectral func-tion usually appears at?k in both the SCBA as well as results
from exact diagonalization.Note that these results are not consistent with ARPES which exhibits an isotropic disper-sion around k0,and rather broad spectral features.Thus,to account for the former,the inclusion of second(t?)and third (t?)nearest-neighbor hoppings to the t-J model have been proposed in the literature.2,14–16However,this approach is meaningful only when the quasiparticle description holds, i.e.,only if a sharp quasiparticle peak exists at?k in the t-J model.As illustrated in Fig.1,if in the thermodynamic limit, the spectral function for a given momentum k does not show a sharp quasiparticle peak,then,notwithstanding how accu-rately?k is determined by various theoretical methods,it has no experimental implication.For,in this case,the higher energy?k?at the broad‘‘peak’’in Fig.1,which is observable experimentally,may have nothing to do with the anisotropic ?k.
On more general grounds,the breakdown of the Landau-Fermi quasiparticle picture has been discussed by Anderson for a doped Mott insulator in the presence of an upper Hub-bard band.17He argues that the quasiparticle weight Z van-ishes due to unrenormalizable Fermi-surface phase shifts in-duced when a particle is injected into the Mott insulator. Indeed,based on a rigorous formulation of the single-electron Green’s function in the one-hole case using the t-J model,it has been demonstrated18,19that the quasiparticle weight Z at the Fermi surface must vanish in the thermody-namic limit due to the presence of the phase string effect. Such a phase string effect can be considered as the equiva-
PHYSICAL REVIEW B,VOLUME63,075102
lent of the phase shifts proposed by Anderson in the Hubbard model.
This paper concerns the effect of the aforementioned phase string on the dynamics of a single hole introduced in an antiferromagnet.We show how the phase string leads to the frustration of kinetic energy of the hole.We then show that the phase string effect is related to spin-charge separa-tion and that the charge carrier is actually a spinless holon.We ?nd that the holon propagator is localized in space,ow-ing to the phase string.This is in contrast to the prediction of SCBA that the hole behaves as a Landau quasiparticle.Our result for the holon propagator is consistent with an earlier conclusion that the quasiparticle weight is zero for the doped hole.18,19It does not necessarily contradict ?nite-size calcu-lations,as the localization length scale turns out to be much larger than typical sample sizes in numerical studies.We ?nd the only coherent object to be a neutral spinon excitation created by the doped hole whose energy spectrum is respon-sible for an isotropic ‘‘quasiparticle’’dispersion.Thus,our results provide a natural explanation of the ARPES results and support the conjecture made in Ref.6.We also discuss how the observed line shapes re?ect spin-charge separation,and ?nally,in the Appendix,how the remnant Fermi-surface structure may be understood as a peculiar consequence of the phase string effect at higher energies.
II.PHASE STRING:THE KEY EFFECT INDUCED BY
THE MOTION OF A HOLE
In this section we examine the effects induced by the motion of a single hole in an antiferromagnetic background.In Sec.II A we shall review a few basic results of the slave-fermion formalism.We then go on to discuss the effect of the phase string on the kinetic energy of the hole,spin-charge separation,and the localization of the holon due to the phase string.
A.Slave-fermion formalism of the t -J model
We begin with the slave-fermion representation c i ?
?f i ?b i ?(??)i
?Refs.20and 21?and express the t -J model H t ?J ?H t ?H J in the following form:
H J ??
J
2
??i j ?
???i j s ????i j s ?2.1?
with
??i j s ?
??
b i ?b j ??,?2.2?
and
H t ??t
??i j ?
B ?i j f i ?f j ?H.c.,
?2.3?
with
B
?i j ???
?b j ??b i ?.?2.4?
At half ?lling,the bosonic resonating-valence-bond ?RVB ?description given by Liang,Doucot,and Anderson 22has provided by far the most accurate picture ?see Fig.2?for both long-range as well as short-range antiferromagnetic ?AF ?correlations in two dimensions ?2D ?.
In this theory,it is found 22,23that the long-range AF cor-relations,including the AF long-range order ?AFLRO ?oc-curring in the thermodynamic limit,constitute only a small fraction of the ground-state energy and the dominant contri-bution mainly comes from the short-range RVB correlations.Thus,the ground state at half-?lling may be regarded as AFLRO ?RVB,of which AFLRO is the most vulnerable part easily removed by either temperature or doping with little energy cost.The mean-?eld version of this bosonic RVB description is known as the Schwinger-boson mean-?eld theory ?SBMFT ?.24This theory works quite well at half ?lling,and is characterized by a bosonic RVB order
parameter
FIG.1.Schematic illustration of a spectral function at a given k in which the quasiparticle weight Z k ?0at the energy bottom ?k .
Here the ‘‘quasiparticle’’peak at ?k
?has nothing to do with the Landau-Fermi
quasiparticle.
FIG.2.The resonating-valence-bond picture ?Refs.22and 23?of bosonic spins provides a highly accurate description of both short-range and long-range antiferromagnetic spin correlations in the Heisenberg model.
WENG,MUTHUKUMAR,SHENG,AND TING PHYSICAL REVIEW B 63075102
?s????i j s? 0.?2.5?But away from half?lling,the problem is highly non-trivial.The reason can be attributed to the fact that the hop-ping integral?B?i j??0in H t.This is generally true due to
the sign?appearing in Eq.?2.4?.So the motion of the hole will be very sensitive to how the spin back?ow B?i j is treated which is a nonperturbative problem and is the key issue to be dealt with in the present work.
In the SCBA approach,7–10the hole can acquire some kinetic energy through the dynamic?uctuations of B?i j.In this approach,only the long-wavelength?uctuations associ-ated with AFLRO is considered,where B?i j is approximated in large-S?spin wave?expansion8by
B?i j?B?i j LSW?b0?
?
??b j???b i??,?2.6?
in which b0denotes the condensed part of the Schwinger
boson?eld,corresponding to AFLRO.25Now,the hopping of the hole is assisted by the?uctuations of B?LSW.This is the
idea behind the SCBA,and within this approach it has been
found that the hole behaves just like a Landau quasiparticle, known as the spin-polaron,with four Fermi points at k0?(??/2,??/2).7–10We reemphasize that within this ap-proximation only the long-wavelength?uctuations associated
with AFLRO are involved,and the dominant short-range
RVB correlations,which are independent of AFLRO charac-terized by b0 0,are completely neglected.
The validity of the SCBA approach is based on the pre-
sumption that spin mismatches,described by the spin back-?ow B?i j induced by the hopping of the hole,can be repaired through the spin?ip process in H J.Thus,the?nal state of the hole,after traversing a closed path through the antiferro-magnetic background,is identical to its initial state.This would be true if one focuses only on,say,the z?component of the spins.But since we are dealing with a quantum spin system in which each spin has three components that do not commute with one another,there will actually be three com-ponents in the spin mismatches induced by the motion of the hole.For the spin-1case,it has been explicitly proven18that such stringlike spin defects cannot be simultaneously re-paired through H J.Once the spin con?guration?i.e.,the z?component?disordered by the hole hopping is restored by spin?ips at low energy,a string defect in the transverse components remains,which is described by a sequence of signs in the quantum description of the hole.This defect is called the phase string.18The effect of this phase string,as we shall see in Secs.II B and II C manifests itself both in the expression for the kinetic energy of the hole as well as its propagator.
B.Effect of the phase string on the energy of the hole
In this section we shall demonstrate that the total energy at momentum k for the one-hole case can be exactly formu-lated as
E k?E0?
t
N
?
i j
e i k?(r i?r j)M i j,?2.7?where
M i j???c????M?c;??????1?N c↓.?2.8?
Here,E0denotes the spin ground-state energy with the hole being?xed at a given lattice site.The energy gain due to the hopping arises solely from the second term.In the expression for M i j,the summations run over all the possible paths of the hole connecting i and j,?c?,as well as spin con?gura-tions,???.The weight functional M is positive semi-de?nite,
M?c;????у0?2.9?such that the phase factor(?1)N c↓is‘‘uncompensated’’in Eq.?2.8?.Here N c↓counts the total number of↓spins?or↑spins by symmetry?being exchanged with the hole moving along the path c.As illustrated in Fig.3,(?1)N c↓????(?1)?(?1)?(?1)????is the phase string on the path c, which was?rst identi?ed in the exact formulation of the single-electron Green’s function.18Later we shall see that, owing to the factor(?1)N c↓,the lowest energy of E k is ob-tained for k?k0,consistent with numerical calculations.11–13 From Eqs.?2.7?,?2.8?,and?2.9?,we come to an important conclusion.Without the phase string factor(?1)N c↓,the total energy would certainly be lower?as Mу0).Thus,(?1)N c↓represents the frustration on the kinetic energy of the hole. This effect is?i?irreparable as no other signs can be gener-ated from the spin background to compensate it;?ii?singular since a change of N c↓by?1will lead to a maximal change in(?1)N c↓;and?iii?thus expected to dominate the low-energy dynamics of the hole.A similar effect is well known in fermionic systems where each fermion’s path is also weighted by a‘‘phase string’’determined by the number of fermions‘‘exchanged’’with it.The difference in this case is that the‘‘exchange’’is between two different species,
the FIG.3.Phase string as a sequence of signs on the hole path c, determined by the index of each spin exchanged with the hole at every step of hopping.
SPIN-CHARGE SEPARATION IN THE SINGLE-HOLE-...PHYSICAL REVIEW B63075102
hole and spins.Therefore,such a phase string effect implies an intrinsic mutual statistics between these two degrees of freedom.19
The proof of Eqs.?2.7?–?2.9?is straightforward.We use the Wigner-Brillouin formula,
E k?E0???0?k???H t?H t G J?E k?H t????????0?k??,
?2.10?where G J(E)?1/(E?H J)and??????excludes??0?as the intermediate state.Here??0(k)??1/?N?i e i k?r i??0(i)?with ??0(i)?denoting the ground state of H J with the hole local-ized at a site i,viz.,H J??0(i)??E0??0(i)?.One can expand ??0(i)?in terms of the complete spin-hole basis???;(i)??(?being a spin con?guration with the hole at site i)as??0(i)??????i??;(i)?.As shown in Refs.18and19,??iу0,which means that the Marshall sign rule21still applies to the doped ground state if the hole is not moving.By inserting the com-plete set of basis states and following the steps outlined in Ref.18for calculating the single-hole propagator,one can easily obtain Eq.?2.7?,with the weight functional
M?c;????
???i???j?s?1K?1??s?1;?m s??P?G J?E k?P???s;?m s????t?,
?2.11?in which?s and?s?1corresponds to spin con?gurations in intermediate states,and the hole site m s is on a path c con-necting two arbitrary sites i and j:m0?i,m1,???,m K ?j(?0??,?K???).Following Ref.18,we can show that ??s;(m s)?P?G J(E)P???s?1;(m s)?р0as long as E?E0?note that the projection operator P??1???0???0?has no effect in the thermodynamic limit N→?).Since we are interested in low-energy states E k?E0,the weight functional M in Eq.?2.11?is always positive semide?nite.
C.Phase string effect and spin-charge separation
In Sec.II B we showed that the phase string manifests itself as irreparable sign?phase?frustrations induced by the hole motion.In this section we shall establish an intrinsic connection between such a phase string and spin-charge separation.
To this end let us?rst consider the origin of the phase string factor(?1)N c↓in Eq.?2.8?.Equation?2.4?,de?ning B?i j,can be rewritten as
B?i j??B i j0?e i??i j,?2.12?where
B i j0???b j??b i??2.13?and
??i j????/2??1??i j?.?2.14?Here?i j?1(?1),if an↑(↓)spinon is exchanged with the holon at the link(i j).For products around consecutive links enclosing a loop?,
?
?
B?i j B?jk???B?li????B i j0B jk0???B li0?exp?i?????,?2.15?with
exp?i????
??e i[??i j???jk???????li]???1?N?↓,?2.16?
where N?↓denotes the total number of↓spins exchanged with the hole along the loop?.Thus,the phase??i j of the spinon back?ow operator?2.12?is the source of the phase string factor in Eq.?2.8?.This is illustrated by the inset in Fig.3.
Since the ground state satis?es the Marshall sign rule,21it is easy to see that
???B i j0B jk0???B li0?
half?lling
?0.?2.17?
?Note that the Marshall sign is totally gauged away in the de?nition of b i?by the sign factor(??)i in the slave-fermion decomposition.?19This is of course consistent with the previous conclusion that the nontrivial phases in the low-energy states all come from the phase string.A hole slowly hopping around the loop?will then acquire a Berry’s phase ??given by
???Im ln???B?i j B?jk???B?li?half?lling
?Im ln?exp?i??????half?lling.?2.18?
So the phase string effect generally leads to a nontrivial Ber-ry’s phase picked up by the hole,as opposed to the quasi-particle picture?of SCBA,for instance?in which the states of the hole before and after traversing a closed path are identi-cal.
Now that we have established the connection between the phase string effect and the spinon back?ow,we are in a po-sition to discuss spin-charge separation.Let us initially sup-pose that the hole behaves like a quasiparticle with both charge and spin quantum numbers.This means that the holon and spinon should be con?ned together.In this case totally one↑(↓)spinon will have to be effectively‘‘transferred’’back from the?nal location of the hole to the initial location to ensure a precise spin quantum number↓(↑)being trans-ported with the hole.It then requires that at each step of the holon hopping,the spinon back?ow is fully polarized,only to involve a↑(↓)spinon being‘‘transferred’’backward. Otherwise,since the spinon back?ow or the phase string ef-fect cannot be‘‘repaired,’’any local?uctuations of the spin polarization of the back?ow spinons,no matter how weak they are,will be accumulated to become arbitrarily large at a suf?ciently long path to invalidate that the hole carries a
WENG,MUTHUKUMAR,SHENG,AND TING PHYSICAL REVIEW B63075102
precise spin quantum number s?1/2.In other words,for the
spin-charge con?nement picture to hold,one must?nd that N c↓?0,or equals the total number of links on any path c, such that the phase string factor(?1)N c↓becomes trivial no
matter how long the path is.But based on Eq.?2.11?one can
easily rule out such a scenario,which imposes the extreme restriction that the probability for any other choices of N c↓vanishes,since an equal probability for both kinds of spinon back?ow is explicitly given in the hopping term?2.3?.In fact,an analysis18,19of the weight functional in the single-electron Green’s function has already led to the conclusion that the phase string effect must be nontrivial?which actually causes the spectral weight Z to vanish as shown in Refs.18 and19?.
Therefore,the irreparable nontrivial phase string effect
directly leads to a true spin-charge separation in the single-
hole doped Mott antiferromagnet.It con?rms the conjecture
made by Anderson.17We note that spin-charge separation
has also been discussed in some exact diagonalization ap-proaches for momenta close to(0,?).15,16In the following, we will go a step further and discuss some unique features associated with spin-charge separation.
Let us de?ne the holon propagator G h in energy space, G h(E)??f j G(E)f i??half?lling,where G(E)?1/(E?H t?J). On expanding in terms of H t,G(E)?G J?G J H t G J????, we get
G h?j,i;E????c????s?1K G J??t?B?m s m s?1?G J?half?lling
???c???s??S?c???s???half?lling??1?N c↓,?2.19?
where S?c(??s?)?…?s?1K G J(?t)?b m
s?1?s
?b
m s?s ?…G J with N c↓
??s(1??s)/2.In Eq.?2.19?,c denotes a path connecting two sites i and j,and m s in the de?nition of S?c is a lattice site on any path c.As with the the positive semide?nite func-tional M in the expression?2.8?for E k,one can easily prove that?S?c?у0for energies E?E0.This means that there are no other sources of phases at low energies to repair the phase
string factor(?1)N c↓.It should be noted that the single-electron Green’s function for the one-hole case has been ex-actly formulated previously in a very similar fashion.18 There,it was found that each hole path is also modulated by the same phase string(?1)N c↓.This result taken in conjunc-tion with Eq.?2.19?shows that the effect of the phase string is entirely in the holon sector,while the spinon released from the hole is not directly associated with such phase frustra-tions.Such a picture is shown in Fig.4.This is not entirely surprising,as we do not expect the motion of a single hole to affect the?thermodynamically large?spin subsystem,except possibly at short-time scales or high energies.
D.Localization of the holon due to the phase string effect
Thus far,we have discussed the general properties of the phase string effect in a rigorous form.To further study the one-hole problem in a quantitative way,we need a suitable framework for approximation.As mentioned earlier,the mean-?eld version of the bosonic RVB theory?SBMFT?provides24a fairly good description of the undoped antifer-romagnet.We now assume,consistent with the discussion so far,that the presence of one hole does not alter the low-energy properties of the spin subsystem as the irreparable phase string is to be solely picked up by the hole.In the following we shall discuss a direct consequence of the phase string effect on the charge part within this approximation:the localization of the holon.
At half?lling,SBMFT characterized by Eq.?2.5?is de-scribed by the Bogoliubov transformation24
b i??
1
?N
?
k
?k?e i?k?r i?u k?k??v k?k??
??,?2.20?
where?k??is an operator that creates an elementary spinon excitation with a gapless spectrum at T?0?,
E k s?2.32J?1??k2,?2.21?and u k?1/?2(2.32J/E k s?1)1/2,v k?1/?2(2.32J/E k s ?1)1/2sgn(?k),with?k?(cos k x?cos k y)/2.Within this mean-?eld theory,it is easy to verify that?b i↑?b j↑???b i↓?b j↓??0.If we use this result naively,when there are N?1spins?and a hole?,we would conclude?erroneously?that B0??B i j0??0,namely,the amplitude of the hopping in-tegral vanishes.This is incorrect because the hopping term connects two spin subspaces,corresponding to the hole at site i and j,respectively,which are not necessarily identical in symmetry.This subtlety has to be incorporated in any calculation,as will be done below.
As a?rst step,let us go back to the case of half?lling. Here it is important to recognize that the factor?k?in Eq.?2.20?which satis?es??????*and????1cannot be com-pletely determined at the level of mean-?eld theory,i.e.,the mean-?eld order parameter?b i?b j???is independent of the choice of?k?.Therefore,there is a hidden symmetry in SBMFT,which is related to the exact local particle-hole in-variance of the system as to be discussed later.
We now exploit this symmetry in SBMFT for the case when there is one hole.Fixing the position of the hole,one may de?ne a subspace for the spins,which,at the level of mean-?eld theory,is again described by the Bogoliubov transformation?2.20?.It should be remembered that Eq.?2.20?now describes an N?1
spin subspace.By choosing FIG.4.Spin-charge separation in the single-hole case:the in-jected hole decays into a neutral spinon and a spinless holon,and the holon will pick up the full effect of phase string.Representing the spinon back?ow effect,the irreparable phase string ensures spin-charge separation as discussed in the text.
SPIN-CHARGE SEPARATION IN THE SINGLE-HOLE-...PHYSICAL REVIEW B63075102
?k ????sgn(?k )?k h ,where k h ?0if the hole is on the even
sublattice and k h ?1if the hole is on the odd sublattice site,one has ?k ?→?sgn(?k )?k ?when the hole hops between the
sublattices.26Then noting that in B i j 0,b j ??
,and b i ?belong to two different spin subspaces,one obtains
B 0?
2N
?k 0
??k ?v k 2
?0.4.?2.22?
It is easy to verify that the above choice of ?k ?optimizes B 0.
Thus we obtain a ?nite amplitude of the hopping integral for the motion of the holon between two sublattices.?Note that in the summation of ?2.22?,k ?0has been removed exclud-ing the b https://www.doczj.com/doc/d95579454.html,ing Eq.?2.4?,one can easily see that b 0part has no contribution due to the sign in ?.?The mean-?eld result remains approximately the same for the su-perexchange term H J in which the holon position is ?xed and ?k plays no role.
This hopping amplitude B 0 0is consistent with ?s 0,and we may understand this in the following way.Physi-cally,each spin subspace has a hidden local particle-hole symmetry,b i ?→b i ???.It is exact and can be preserved in the RVB description if the no double occupancy constraint is strictly implemented locally.Let us assume that the holon is,say,at an odd sublattice site.Then,on performing a trans-formation b i ?→b i ???only in the corresponding spin sub-space ,it is easy to see that B i j 0at the hopping bond trans-forms into the RVB order parameter ?s .Note that at the mean-?eld level in SBMFT,the local hard-core constraint is relaxed where the particle-hole symmetry is no longer exact.But it can be checked that the symmetry ?k ?→?sgn(?k )?k ?in SBMFT still approximately corresponds to b i ?→b i ???at the global level according to Eq.?2.20?.?It would be exact if ?u k ???v k ?).It tells us that the direct hop-ping term for the holon indeed originates from local RVB spin pairing with a particle-hole symmetry in each spin sub-space.
With B 0 0,G h in the ?rst line of Eq.?2.19?may be written,in the limit of E →??,as
G h ?E →????
??c ?
g h c exp ?i ?c ???half ?lling
,
?2.23?
where g h c ?2K ?S ?c ?half ?lling .Note that in E →??limit G J
→1/E becomes commutable with e i ??
.We can now calculate
the phase string average ?e i ?c ??
?half ?lling explicitly as
exp ?i
?c
???
half ?lling
?e i ??c ??
?exp ?i
?c ?
??
????????e i k 0?(r i ?r j )
?exp ??
1
2
???
c
??
????????2
??
,
?2.24?
where ???c (???????)?2??(?2/2)?(?i c :S i z :)2?,and :S i z aS i
z ??S i z ?.Using the results for ?S i z S j z ?from SBMFT,
24
one ?nds in the large ?r i j ?limit the asymptotic form for expres-sion ?2.24?and thus,the holon propagator as
G h ?j ,i ;E ??e
i k 0?(r i ?r j )e
?
?r i ?r j ?
?L
.?2.25?
The localization length is determined numerically,for the
case E ???,as ?L (E ???)?2.2a for r i j parallel to the x or y axis.?Here a is the lattice constant.?
The exponential decay ?2.25?of the holon propagator,a typical characterization of localization phenomenon ,is fun-damentally different from the power-law decay for the propagator generally expected when the hole behaves like a well-de?ned quasiparticle.The very fact that the holon propagator behaves like Eq.?2.25?as E →??is enough to invalidate conventional quasiparticle behavior.As in conven-tional localization problems,we expect ?L (E )to increase with the energy E and to represent the true localization length scale at E уE G (E G is the ground-state energy ?.Later,we shall determine the localization length ?L (E )numeri-cally,in the physical regime of E .We ?nd it to be generally larger than the overall scales of sample sizes (?6a ?6a )used in exact-diagonalization calculations.So,the hole local-ization caused by the phase string effect cannot be directly detected by exact diagonalization,owing to the limitation of the sample size.On the contrary,as in conventional localiza-tion problems,a localized electron can be mistaken for a delocalized electron simply because the sample sizes are smaller than the localization length.Thus,we argue that the well-de?ned quasiparticle peak seen in ?nite size calcula-tions is an artifact of small sample sizes and cannot persist at scales beyond ?L .
III.SPECTRAL FUNCTION
A.Effective theory
As pointed out earlier,the bosonic spin RVB pairing
gives an extremely good description of the undoped antifer-romagnet for both short-range and long-range spin-spin cor-relations.The direct hopping of the holon originates from short-range RVB pairing with a local particle-hole symme-try.Unlike the long-range spin correlations,the short-range correlations are not sensitive to doping and the local RVB order parameter ?s provides a certain local ‘‘rigidity’’that underpins the doped antiferromagnet,as long as the average spacing between the holes is larger than the distance between nearest neighbors.Indeed,such a direct hopping term can persist into the metallic ?superconducting ?phase at ?nite doping,as discussed in Ref.27.However,unlike the metallic system,the one-hole case is different as we do not expect the AF spin background to change at thermodynamic scales.As discussed in Sec.II,one may,to leading order,assume the spin background to be the same as that at half ?lling.The feedback effect on the spin part at high-energy,short-distance scales will be considered in the Appendix.
In Sec.II we saw that the holon picks up the effect of the phase string and that the effective Hamiltonian can be writ-ten as
WENG,MUTHUKUMAR,SHENG,AND TING PHYSICAL REVIEW B 63075102
H h??t h?
?i j?
e i??i j
f i?f j?H.c.?3.1?with t h?B0t?0.4t.Here,the nontrivial effect arises solely from the phase??i j,re?ectin
g the irreparable phase string effect.In terms of Eq.?2.14?,we may rewrite
e i??i j?e i k0?(r i?r j)[1??i j]?e i k0?(r i?r j)e?ia i j,?3.2?where
k0????2a,??2a??3.3?
and a i j?k0?(r i?r j)??i j?.
To characterize the strength of a i j,let us consider the gauge invariant quantity??a i j,i.e.,the?ctitious‘‘mag-netic’’?ux seen by the holon hopping around a plaquette:i →i?x?→i?x??y?→i?y?→i.One can easily get
??a i j????S i?x?z?S i?x??y?
z?S
i?y?
z?S
i
z?.?3.4?
Generally,???a i j??0,and the strength of the quadratic ?uctuations is given by
????a i j?2???2?1?4?S i?S i?x??y???.?3.5?
Using the SBMFT one can estimate??(??a i j)2??0.86?and?nd that,for two plaquettes separated far away from each other?i.e.,the distance R12?a),
????a i j?1???a lk?2??O?a4R124?.?3.6?
Note that the spatial correlations between the?uxes thread-ing through different plaquettes fall off rapidly in Eq.?3.6?. This is because the contribution from the long-range AF ?uctuations is strongly canceled out in Eq.?3.4?.Similarly, the correlations of?uxes per plaquettes at different times also decay very quickly.Thus,as the?rst order of approxi-mation one may treat a i j as a gauge?eld describing random ?uxes in the white-noise limit with the strength controlled by Eq.?3.5?.?The phase string effect beyond the random?ux approximation is brie?y discussed in the Appendix in con-junction with the momentum dependence of the energy-integrated spectral function.?
In the effective model?3.1?,the effect from the longer-range spin correlations involving the AFLRO,which in?u-ence the hopping of the holon through Eq.?2.6?,has been omitted.This process has been considered in the SCBA ap-proach as the sole source assisting the holon hopping.In the following we reexamine it in the presence of the bare holon term?3.1?.With the Bose condensate b0 0?AFLRO?,one may express c i??(??)i cˉi??(??)i f i?:b i?:with cˉi??b0f i?and:b i?ab i??b0.Then,Eq.?2.6?leads to the fol-lowing hopping Hamiltonian:
H h LSW??t??i j????cˉi?:b j??:f j?f i?:b i?:cˉj????H.c.
?3.7?If there were no bare hopping?3.1?for the holon,H h LSW would represent a virtual process,which,by the SCBA treatment,7–10would give rise to the well-known quasiparti-cle description for cˉi?.But in the presence of Eq.?3.1?, H h LSW literally describes the process for cˉ??the‘‘quasiparti-cle’’?to decay into a holon-spinon pair.In this case,the propagator Gˉe for cˉ?will no longer behave like the one for a dressed quasiparticle found in SCBA.In contrast,to the leading-order approximation,it will be simply proportional to the propagator of f i?:b i?:to be discussed below.So in the following we do not consider H h LSW in Eq.?3.7?and simply switch cˉi?off,by assuming either the sample size to be large but?nite or T?0?,such that b0?0without loss of gener-ality.
B.Spectral function
In this section we shall show that the main features ob-served in ARPES can be described within our formalism.We attribute the broad spectra that are observed to the fact that the physical electron is a convolution of spinon and holon excitations.We show that the dispersion of the photoelectron is governed by the dispersion of the spinon,and conse-quently,isotropic.We also show that the phase string plays a crucial role in causing the sharpest spectra at low binding energy locating at(??/2,??/2)?i.e.,the‘‘Fermi points’’?.
The single-electron propagator may be expressed in the following decomposition form:
G e?iG b?G h,?3.8?where
G b?i,j;t???i????i?j?T t b i??t?b j???0??,?3.9?and
G h?i,j;t???i?T t f i??t?f j?0??.?3.10?Here we mainly focus on the properties of the spectral func-tion de?ned by A e(k,?)??(1/?)Im G e(k,?)sgn(?), which can be measured by https://www.doczj.com/doc/d95579454.html,ing the decomposition ?3.8?,one?nds the convolution law
A e?k,????????
1
N
?
k?
?
?
d???h?k??k,??
????b?k?,????3.11?at T?0?where?b and?h are the spectral function corre-sponding to G b and G h,respectively.
By using Eq.?2.20?one can easily obtain
Im G b????u k2????E k s??v k2????E k s??.?3.12?As noted above,in the one-hole case this half-?lling mean-?eld propagator should not be affected thermodynamically
SPIN-CHARGE SEPARATION IN THE SINGLE-HOLE-...PHYSICAL REVIEW B63075102
by the motion of the single holon.Then the corresponding electron spectral function is written as
A e
?k ,???
1
N
?k
?
v k ?2?h ?k ??k ,?E k ?s
???,?3.13?
where the condition ?h 0only at ?у0is used which de-?nes the bottom of the holon band at ??0.
The overall feature of A e (k ,?)versus ?is shown in Fig.5at different k ’s along ?0,0?to k 0.The whole energy range of the spectral function is about 16J ?2.24eV ?for J ?0.14eV).Here we have chosen t h ?2J (t ?5J )in Eq.?3.1?in obtaining the holon spectral function ?h which is calculated numerically by exactly diagonalizing H h under random ?ux with ???a i j ?р0.86?in the white-noise limit.The sample size is 32?32.
Even though not ?function like,the spectral function does show peaks which become sharper near both energy bottom and top as the momentum approaches k 0.According to Eq.?3.1?,the bottom and top of the holon band are near the momenta shifted away from ?0,0?and (?,?),respec-tively,by k 0,where the spectral function ?h is sharpest in contrast to the broadest feature near the band center due to
the random ?ux.On the other hand,the spinon spectrum E k s
is maximum at k 0and vanishes at momenta ?0,0?and (?,?).The convolution law of Eq.?3.11?then combines the contri-butions from the holon and spinon to result in Fig.5.Note that the peaks are asymmetric at the top and bottom of the band.The effect of the spinon spectrum is most visible at lower binding energies,as will be further discussed below.A similar asymmetric structure in one dimension has been found in Ref.28.
Let us now focus on the structure of A e at low binding energies in comparison with ARPES measurements on Sr 2CuO 2Cl 2?Refs.1and 2?and Ca 2CuO 2Cl 2.3In the left panel of Fig.6,we plot A e within the energy range of 8J ?1.1eV at k positions along a line from ?0,0?to (?/2,?/2)and then from (?/2,?/2)to (?,0).The peak or edge posi-tion shows an isotropic dispersion along ?0,0?to (?/2,?/2)and from (?/2,?/2)to (?,0),consistent with the experi-
ments.Such a dispersion has a bandwidth about 2J and is
clearly correlated with the spinon spectrum E k ?k 0s
.The latter is marked by small bars at different k ’s where the position of
the minimum E k ?k 0s
at k 0is ?xed around ??0.7J as a ref-erence point.In the right panel of Fig.6,a plot of A e along ?0,0?and (0,?)is shown where the peak is replaced by an edge which looks dispersionless,also in good agreement with the experiment.Indeed,a very ?at ?only about 13%
change ?E k ?k 0s
along ?0,0?to (0,?)is indicated in the ?gure
by the small bars.In Fig.7the spinon spectrum E k ?k 0
s
?ts
FIG.5.The full shape of the spectral function calculated at k ?(?/2,?/2),(?/4,?/4),and (0,0).Note the whole energy range extends over 16J ?2.24eV ?for t ?5J ,J ?0.14
eV).
FIG.6.The spectral function at low binding energy along dif-ferent momentum scans.The small bars mark the spinon spectrum
E k ?k 0s ??0with ?0?0.7J
.
FIG.7.The ‘‘quasiparticle’’spectrum determined by the
ARPES ?Ref.3??open square ?and by the spinon spectrum E k ?k 0s
?solid curve ?.
WENG,MUTHUKUMAR,SHENG,AND TING PHYSICAL REVIEW B 63075102
the observed ARPES ‘‘quasiparticle’’spectrum data reason-ably well over the whole Brillouin zone along k 0(?)to ?0,0?(?)and (0,?)?X ??which are symmetric in our theory ?with J ?0.14eV.Note that the low-energy scale is determined by J instead of t and the features shown in Fig.6are not sensi-tive to t .Thus,second or further neighbor hopping terms are not expected to play as important a role as they do in deter-mining the energy bottom ?k ,shown in Fig.1.
The reason that the low-energy peak or edge of the spec-tral function is correlated with the spinon spectrum can be easily understood by noting the fact that ?h (k ,?)becomes the sharpest near the bottom ??0with k ?k 0which con-tributes to A e in Eq.?3.13?at k ??k ?k 0and ???E k ?k 0.In Fig.8?a ?the spectral function along ?0,0?,k 0is shown when the maximal strength of ???a i j ?is reduced from 0.86?to 0.1?.Here the correlation between the low-energy peak or edge positions and the spinon spectrum is even more appar-ent as the holon spectral function ?h becomes sharper near ??0and k 0.The evolution from a peak to an edge as k moves away from k 0is because the spectral function of the holon is quickly broadened away from the band bottom in the presence of the random ?ux.Note that compared to the experiment the peak structure in Fig.8?a ?is a bit too sharp which implies that the actual strength of ???a i j ?should be closer to our estimation used in Fig.6.
The line shape of the spectral function shown in Figs.6and 8?a ?looks strikingly similar to the ARPES measure-ments in Sr 2CuO 2Cl 2and Ca 2CuO 2Cl 2.1–5It re?ects essen-tially the convolution law of spinon and holon,i.e.,the spin-
charge separation.But we would like to point out that the simple convolution law is not enough.Here the coherence of the spinon in contrast to the incoherent holon is key to the characteristic features of the line shape and the ‘‘dispersion’’of the peak or edge structure.To illustrate this point,we
replace the coherent factor v k 2
in Eq.?3.13?by a constant
?i.e.,v k 2
?1),and recalculate the spectral function which is plotted in Fig.8?b ?along ?0,0?,k 0.One sees that the whole low-energy peak-edge feature in the left panel of Fig.6and Fig.8?a ?totally disappears in Fig.8?b ?.In this case,the summation in Eq.?3.13?smears out the peak structure and A e is more or less like the density of states for the holon.So the coherent factor v 2in the spinon propagator is crucial for the ‘‘quasiparticle’’peak to emerge in the spin-charge sepa-ration formulation of the spectral function,which is the unique result of the bosonic RVB description of spins.This explains why the correct line shape has not been directly obtained in the slave-boson formalism,even though the pre-diction that the ‘‘quasiparticle’’spectrum obtained in ARPES actually corresponds to the spinon spectrum was ?rst made 6there.
The incoherence of the holon is also an important factor as discussed above.It is well known that a particle must be generally localized,at least in the low-energy regime,in the presence of the random ?ux governed by H h in Eq.?3.1?.We have checked the localization lengths corresponding to the case of Fig.6using standard methods.29The localization length quickly jumps from 4–15?in lattice units ?to 36–50near the holon band edge which covers an energy range re-lated to the low-energy peaks of the spectral function in Fig.6.As noted before,the localization length scale of the holon is generally much larger than the maximum sample sizes (?6?6)in numerical exact-diagonalization calculations.12Thus,numerical calculations providing a ‘‘metallic’’quasi-particle picture should be irrelevant to the true picture at large length scales.
Finally,to conclude our discussion of ARPES in the Mott insulator,we turn to the experimental results of Ronning et al.3These authors identify a ‘‘remnant Fermi surface’’in the insulator from ARPES measurements:they de?ne the so-called relative momentum distribution
n k r ??0??
?
?00
d ??
A e
?k ,??,?3.14?
with the cutoff energy ?0??0.5eV,then identify ‘‘k F ’’by locating the position where n k r drops suddenly.Then a rem-nant Fermi surface is found as the contour of steepest descent of n k r .Such a remnant Fermi surface roughly coincides with the large Fermi surface expected for a free-electron gas at half-?lling concentration.It should be emphasized that this contour is not an equal energy contour.In fact,the peak ?or edge ?of the spectral function disperses at momenta along the remnant Fermi surface as much as that shown in Fig.7.So the remnant Fermi surface mainly indicates a strong momentum dependence of the energy-integrated spectral function n k r .We believe this is due to the effect of the mo-bile hole on the spin background ?at very short time scales ?.So far we have not considered the in?uence of the
phase
FIG.8.?a ?The spectral function similar to the left panel of Fig.6,but with the random ?ux strength per plaquette reduced to 0.1??see text ?.Small bars marked the same spinon spectrum as in Fig.6?but with ?0?0.2J ).?b ?The line shape of the spectral function in the left panel of Fig.6is greatly changed if the spinon coherent
factor v k 2
is replaced by a constant 1.
SPIN-CHARGE SEPARATION IN THE SINGLE-HOLE-...PHYSICAL REVIEW B 63075102
string effect on the spin degrees of freedom.This is based on
the fact that a single hole does not affect the spin background
at the thermodynamic scale.However,the AF background
surrounding the doped hole should be still strongly distorted by the hopping at t?J,which in turn will feed back on the
hole itself through the phase string effect.Obviously,this
happens at short length and time scales.Consequently,one
has to go beyond the effective Hamiltonian?3.1?as well as
the random?ux treatment of the phase string effect.Not
being within the main purview of this paper,we relegate the
discussion of such effects to the Appendix.
IV.CONCLUSIONS AND DISCUSSIONS Although antiferromagnetism in the Mott insulator has
been well understood based on the bosonic RVB description,
the problem of a single hole doped into such a system is
found to be nontrivial.Unlike the spin-polaron picture in
which the hole is predicted to behave like a Landau-Fermi
quasiparticle carrying a?nite-size spin distortion around it,
the real picture for the motion of the doped hole is that it
always picks up a string of signs from the spin background
during its hopping,known as the phase string,which leads to
the destruction of the‘‘coherence’’of the doped hole as a
Landau-Fermi quasiparticle.
The phase string characterizes the effect of spin back?ow
during the motion of the hole.The irreparable nature of
phase string is intimately related to spin-charge separation:
the hole cannot carry a precise spin-1/2quantum number
with it.In contrast,if the holon and spinon were tightly
con?ned together,the phase string effect would become
trivial?reparable?,as is the case when one naively uses the c
operator to replace the spinon-holon decomposition in Eq.?2.3?.Hence,the demonstration that the phase string effect cannot be‘‘healed’’through spin superexchange interaction
at low energies,presented in Sec.II B and Refs.18and19,
points directly to spin-charge separation.It is also found that
the spin back?ow,or equivalently,the phase string leads to
mutual statistics between the hole and spin degrees of free-
dom.That the back?ow of spin current could lead to mutual
statistics and spin-charge separation was also anticipated by
Baskaran.30
In the one-hole case,the phase string effect mainly acts
on the holon part,causing its localization.But the spinon
remains coherent in the bosonic RVB background.Conse-
quently,during its propagation,a bare hole releases the co-
herent spinon constituent whose isotropic dispersion essen-
tially determines the position of the low-energy peak or edge
of the spectral function.On the other hand,spin-charge sepa-
ration characterized by the convolution law of the holon and
spinon propagators is responsible for the intrinsic broad fea-
ture of the spectral function at higher energy.In the phase
string formalism,the singular part of the phase string effect also decides the Fermi points k0in the low-energy,long-time limit as well as the large remnant Fermi surface structure in the high-energy,equal-time limit.We thus obtain a system-atic and natural explanation for the ARPES measurements within the framework of the t-J model.Conversely,one may say that the ARPES experiments have clearly presented evi-dence for spin-charge separation,as emphasized by Ander-son.
We?nd that the‘‘coherence’’of the spinon,re?ected by the factor v k2in SBMFT,plays an important role in determin-ing the ARPES line shapes.A naive convolution without this factor is not enough to explain the line shape observed by ARPES.We also note that the strong temperature depen-dence of the ARPES line shapes over a wide energy range,31 may be easily understood based on the temperature depen-dence of v k2.Details will be presented elsewhere.Finally,we point out that the temperature dependence of v k2is also cru-cial to get the correct behavior of the relaxation rate(1/T1) in nuclear magnetic resonance measurements,spin-spin cor-relation length,and other magnetic properties at half?lling within the SBMFT.
The prediction that the holon as the charge carrier is lo-calized by the phase string effect is also consistent with the cuprate superconductors.It is known that the phase with AFLRO?weakly doped regime?is always an insulator.Ac-cording to our theory,the localization is due to the intrinsic nature of the doped Mott insulator instead of external reasons like the Anderson localization in the presence of impurities.
Note that the localization of the hole is because the phase string is solely picked up by the hole,and the antiferromag-netic background remains the same as at half?lling,thermo-dynamically.At?nite density of holes,both spin and charge degrees of freedom will be affected by the phase string, which can lead to a metallic?superconducting?phase27with-out AFLRO.We emphasize that the irreparable phase string effect always exists,even in the metallic phase.This is be-cause the phase string re?ects the competition between the hopping and superexchange interactions in the t-J model, which has nothing to do with the existence of AFLRO.Thus, the phase string effect will persist at any?nite doping so long as short-range antiferromagnetic correlations persist.19,27
ACKNOWLEDGMENTS
We acknowledge useful discussions with A.Ferraz,T. Tohyama,T.K.Lee,and especially C.Kim and F.Ronning who kindly provided their experimental data.We also thank Barry Wells for discussions on ARPES and useful corre-spondence.Work at Houston was supported in part by Texas ARP Grant No.3652707,the Robert A.Welch Foundation, and the Texas Center for Superconductivity at the University of Houston.V.N.M.is supported by NSF Grant No.DMR-9104873.
APPENDIX A:SHORT-TIME SCALE EFFECTS AND THE‘‘REMNANT FERMI SURFACE’’The holon is localized by phase string in space.But at a short scale within the localization length,the holon may be-have like in the metallic phase at?nite doping where holons are mobile.It has been found19,27that in the metallic phase the phase string effect will in?uence both the spin and charge degrees of freedom in such a way that the correct decompo-sition form for the electron becomes
c i??h i?bˉi?e i??i?string,?A1?
WENG,MUTHUKUMAR,SHENG,AND TING PHYSICAL REVIEW B63075102
where h i?and bˉi?are the‘‘true’’holon and spinon operators and the phase shift?eld e i??i?string precisely keeps track of the nonrepairable phase string effect.In the following we will use this formalism to describe the local,high-energy regime in the one-hole case and show a nontrivial consequence of the phase string effect.
In the one-hole case,the phase shift?eld can be written as e i??i?string?(??)i e(i/2)?i b in which
?i b??l i Im ln?z i?z l?????n l?b?1??A2?
with z i?x i?iy i representing the complex coordinate of a lattice site i and n l?b denoting the spinon number at site l.
In order to understand n k r,let us?rst take?0to??.In this high-energy or equal-time limit,n k r reduces to the mo-mentum distribution n k which is given by
n k?1
N
?
i j
e i k?(r j?r i)?c j??c i??
?1
N
?
i j
e i k?(r j?r i)?bˉj??h j?e i??d r?A?f(r)?h i??0?bˉi??,
?A3?
in which the following expression for the equal-time phase-string factor is used:
e i(1/2)?i b(t)e?i(1/2)?j b(0)?t→0??e i??d r?A?f(r)?A4?with
A?f?r??1
2
?
l????n l?b?1
?z???r?r l??r?r l?2,?A5?
where the path?connects two lattice sites i and j without crossing other lattice sites.Clearly,in the equal-time limit, the momentum structure will be mainly decided by the os-cillation of the phase string factor given in Eq.?A4?.
For the one-hole case,n k in Eq.?A3?is actually trivial and featureless(?1/2).This is because?c i??c j????i j?bˉi??bˉi??using the non-double-occupancy constraint in which no propagation of the holon at a?nite distance can occur at strictly equal time on the half-?lling ground state. On the other hand,n k r for a?nite cutoff?0will involve a ?nite-time holon propagation over some?nite distance.In this case,the phase string factor in Eq.?A4?will show up to determine the basic feature while the rest of the propagator involving holon and spinon will mainly give rise to a broad-ening in the momentum space,depending on how far the holon and spinon constituents can travel under the cutoff?0. At?0???,the momentum broadening would reach in?nity ?as only i?j contributes?such that any momentum structure arising from e i??d r?A?f(r)gets smeared out.But at a large but ?nite??0?the momentum structure due to the phase string factor should show up.Here as an approximation the equal-time phase string factor is still used so long as??0?is suf?-ciently large.
In the spin channel,a line-integral expression similar to Eq.?A4?also appears32in the spin-spin correlation function, leading to the so-called incommensurate antiferromagnetic peaks.Here we can borrow the similar method used in Ref. 32to manipulate the contribution of the phase string factor ?A4?in n k r,which gives rise to four‘‘incommensurate peaks’’at(???,0)and(0,???)in momentum space with ??1.33If this oscillating factor solely decides the momen-tum structure of n k r with the rest term in the propagator
mainly contributing a broadening as discussed above,then one gets a contour plot of n k r in Fig.9in terms of the super-position of the aforementioned four peaks?with??0.75)at an arbitrary broadening?which is presumably controlled by the energy cutoff?0:when?0→??,the broadening in the momentum space should go to in?nity such that n k?1/2). Note that the values of n k r here are only meant for relative comparison.
We see that the overall feature is in qualitative agreement with the experimental data3whose one-quarter portion is also shown in the inset of Fig.9for comparison.Here we remark that experimental data34,35of n k r seem to be photon-energy dependent,indicating the effect of the electron-photon ma-trix element,and there also exists controversies34,35on whether the remnant Fermi surface de?ned near the sharpest drop of n k r in k space is meaningful or not.But in the present approach the momentum dependence of n k r does not repre-sent any real Fermi-surface structure of the Mott antiferro-magnet at half?lling.It only re?ects the superposition of four peaks near(??,0)and(0,??),an enhancement en-tirely coming from the dynamic effect of the doped hole as the result of a careful handling of the phase string effect in the local,high-energy regime.As a prediction,if experimen-tally??0?is taken to suf?ciently higher energy,the momen-tum dependence of n k r should get weaker and weaker and eventually n k r→n k?1/2at?0→??
.
FIG.9.The contour plot of the electron momentum distribution exhibiting a remnant Fermi surface structure.The experimental data ?Ref.3?are shown in the inset at the upper right corner.
SPIN-CHARGE SEPARATION IN THE SINGLE-HOLE-...PHYSICAL REVIEW B63075102
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25For convenience,the magnetization here is to lie in the x-y plane instead of along the z axis as in Ref.8.
26Note that such a hole-position-dependent choice of the phase?
k?is perfectly legitimate as in the sub-Hilbert-space in which the hole position is given,the commutation relations of b,b?remain unchanged.On the other hand,the spin-hole states are simply orthogonal if the hole is at different sites.
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WENG,MUTHUKUMAR,SHENG,AND TING PHYSICAL REVIEW B63075102
《公共管理学》homework（1） 一、名词解释 1.公共管理: 公共管理是指公公组织为解决公共问题，追求公共利益，运用公共权力，通过制定公共政策、有效地实行与监督等，提供公共物品和公共服务，维护公共秩序，对公共事务进行管理的社会活动。 2.公共选择理论公共选择理论是一门介于经济学和政治学之间的新兴交叉学科，它是运用经济学的分析方法来研究政治决策机制如何运作的理论。 3. 公共管理协调指协商、调整公共组织系统与其外部环境之间和系统内部的各种关系，使之权责清晰，分工合作，相互配合，有效地实现公共管理目标和提高整体效能的行为。 4. 公共管理监督是指依法对政府和公共事业组织等公共组织及其工作人员的监察和督导活动。 二、单项选择 1.1926年在美国出版两本权威的行政学教科书《行政学研究导论》《公共行政学原理》的两位学者分别是( B ) 25 A.泰勒和法约尔 B.怀特和威洛比 C.威尔逊和古德诺 D.马克斯?韦伯和赫伯特?西蒙 2.公共选择理论理论对政府的本质和行为的基本假设是( B)
A.社会人 B.经济人 C.自动人 D.复杂人 3.大萧条以后，为资本主义的稳定和发展起到了积极的作用的经济理论是( A ) A.凯恩斯的政府干预理论 B.新自由主义取消政府干预理论 C.亚当?斯密的“小政府”理论 D.古典经济学派的限制政府干预理论 4. 最早建立了比较规范的文官制度的国家是( A ) A.英国 B.法国 C.德国 D.美国 5. 18世纪英国著名经济学家________，在他著名的经济学著作《国富论》中对政府财政的管理范围和职能进行了限定。( C ) A.威廉?配第 B.马歇尔
【导语】中国音乐家协会根据弹奏技巧的难度和音乐表现力等标准，将钢琴弹奏划分为十个等级。初学钢琴、计划等级考试的学员对于钢琴等级考试不是很清楚，下面由小编带领大家认识一下钢琴是个等级考试大全。 中国钢琴考试一共分为十级，因为各地组织机构不同，所以考试时间也不同。一起来看看详细介绍。 1.全国音乐家协会音乐考级委员会组织的考级（每年2次，分别在暑假和寒假进行，报名地点一般在各省的音乐家协会，比如沈阳市的全国钢琴考级就是在辽宁省音乐家协会报名的） 2.中央音乐学院钢琴考级（注：中央音乐学院的钢琴考级没有十级，九级为其最级别，但其九级难度也要比全国的十级好要高，各地应该有报名点，沈阳的刘宁钢琴学校就是中央音乐学院在辽宁地区的一个考点，其他地区也有相应的机构负责代理） 3.上海音乐家协会钢琴考级（上海什么都跟全国不一样，比如高考试卷，所以在上海是不能参加全国音乐家协会的钢琴考级的，每年只有暑假可以考，最高级别也是十级，不过要说明的是，上海的考级曲目难于全国，上海的九级曲目已经是全国十级的曲目了，上海的十级可以相当于全国考级的“十一级”，近年来上海又开发出了一个“演奏级”，其难度比十级还高，供有能力的人来考） 以全国音协的钢琴考级为例，每一个级别都要考查四项技能（四
项都为必考项目，因此不存在练一首曲子可不可以考级的说法，此外曲目是专门指定的，只能从其中选择，不可逃避）： 1.基本功：要求考查你的音阶、琶音的演奏能力，随着级别的升高，升降记号逐渐增加（10级考6升或6降）、音阶和琶音的速度也逐渐加快（10级音阶要求达到每分钟弹奏144个四分音符，即516个十六分音符，相当于每秒8.6个音），音阶和琶音的长度和难度姐会逐渐在增加，双手同向一个八度到最后得双手反向四个八度。 2.练习曲：是最能考验你的演奏水平的一项了，如果你是系统学习钢琴的话，完全可以跟就目前所学的练习曲程度来检验自己符合与哪一个级别。以下是上海音协的1—10级（每一级别高于全国音协一级，即上海的九级相当于全国的十级），你可以自己对照一下：一级：《拜厄钢琴基本教程》全部学完，双手的配合已经较为协调 二级：熟练掌握车尔尼《钢琴初级练习曲》（599）后半部分程度的同时，还能够接触一些比较复杂的节拍和变化 三级：弹到车尔尼《钢琴流畅练习曲》（849）前半部分，手指跑动能够达到一定的流畅度。 四级：谈完车尔尼《钢琴流畅练习曲》（849），达到双手弹奏精准，并具有一定的表演能力 五级：弹到车尔尼《钢琴流畅练习曲》（299）的前半部分，具备
基本练习： 1．音阶（分手、两个八度） 2．分解和弦（三个音一组、分手） C、G、D大调，A、E和声小调 曲目： A组 B组 1．练习曲（Op.599 No.19）……车尔尼 1.练习曲……贝尔科维奇2．巴斯皮耶……亨德尔 2.德国民歌……巴赫 3．忧伤……巴托克 3.奏鸣曲（G大调第四乐章）……海顿 4．俄罗斯民歌……贝多芬 4.诉说……古里特 选曲： 1．浏阳河……唐碧光作曲、陈静斋改编 2．田园曲（Op.100）……布格缪勒 3．儿童游戏……巴托克 全国钢琴演奏二级 基本练习： 1．音阶（分手、两个八度） 2．分解和弦（四个音一级、分手） C、G、 D、A、F大调，A、 E、D和声小调 曲目： A组： B组： 1．练习曲……古里特 1.练习曲（Op.176 No.14）……杜威诺阿2．加沃特舞曲……亨德尔 2.加沃特舞曲……库普兰 3．回旋曲……莫扎特 3.快板……阿尔诺尔德 4．旋律……舒曼 4.儿童献花舞……金爱平 选曲： 1．天真烂漫（Op.100）……布格缪勒 2．苏格兰舞曲……贝多芬 3．爵士小练习……赛贝尔
基本练习： 1．音阶（分手、三个八度） 2．琶音（分手、两个八度） 3．半音阶（分手） C、G、 D、A、 E、B、F大调，A、E、B、D、G、C和声小调 曲目： A组 B组 1．练习曲……勒士豪恩 1.练习曲（Op.37）……雷蒙 2．波罗涅兹舞曲……巴赫 2.库朗特舞曲……亨德尔 3．急板（Op.55 No.1）……库劳 3.快板（Op.36 No.3）……克列门蒂 C大调小奏鸣曲第2乐章 C大调小奏鸣曲第3乐章 4．叙事曲（Op.100）……布格缪勒 4.勇敢的骑士……舒曼 选曲： 1．手摇风琴……肖邦塔科维奇 2．歌曲……泰勒曼 3．甜密的幻想……柴科夫斯基 全国钢琴演奏四级 基本练习： 1．音阶（合手、四个八度） 2．移音（合手、四个八度） 3．半音阶（合手、两个八度） C、G、 D、A、 E、B、 F、bB、bE大调及其关系和声小调 曲目： A组 B组 1．练习曲（Op.46 No.1）……海勒 1.练习曲（Op.849 No.12）……车尔尼2．阿勒曼德舞曲……巴赫 2.二部创意曲（No.4）……巴赫 3．回旋曲（Op.36 No.5）……克列门蒂 3.回旋曲（Op.20 No.1）……杜赛克G大调小奏鸣曲第3乐章 G大调小奏鸣曲第2乐章 4．老祖母的小步舞曲……格里格 4.圆舞曲（Op.12 No.2）……格里格
电大《公共管理学概论》（教育管理本科）形成性考核册参考参考答案(2010) 案例分析答案在最后一页 一、填空 1、公共管理活动公共行政学 2、公共组织社会公共事务公共利益公共权力 3、罗伯特达尔赫伯特西蒙新公共行政学 4、限制政府干预主张政府干预 5、非政府性公益性正规性 6、公共权力公共社会 7、政治实体行动方案和行动准则 8、调节性自我调节性 9、政策宣传政策分解物质和组织准备 10、事实价值 二、选择题 1C 2D 3C 4A 5B 6B 7A 8D 9B 10D 三、简答题 1、什么是公共管理的内涵？P2 所谓公共管理，就是公共组织运用所拥有的公共权力，为有效地实现公共利益，对社会公共事务进行管理的社会活动。主要包括以下几点： （1）公共管理的主体是公共组织 （2）公共管理的客体是社会公共事务 （3）公共管理的目的是实现公共利益 （4）公共管理的过程是公共权利的运作过程 2、政府职能演变经过那几个阶段？P34 （1）限制政府干预 （2）主张政府干预 （3）对政府职能的重新思考 3、简述政府失效理论的基本观点及政府失效的几点表现？P45 政府失效理论的基本观点是对人的“经济人”的假设。即认为人是自利的、理性的，而且每个人都在追求个人利益的最大化，政府公务员也不例外。由此看来，在政治决策过程中，人的一切行为都可看成是经济行为，而使“政府政治过程的目的肯定是增进公共利益的假设”受到质疑而不得不被放弃。 （1）公共政策失效 （2）公共产品供给的低效率 （3）内部性与政府扩张 （4）“寻租”及腐败 4、简述非政府公共组织的基本特征。P49 （1）非政府性 （2）公益性 （3）正规性 （4）专门性 （5）志愿性
公共管理学作业1 一、简答题 1、简述公共管理模式得基本特征 (1)公共利益与个人利益相统一,重在公共利益上。 (2)政府组织与其她公共组织相统一,重在政府组织上。 (3)社会问题管理与资源管理相统一,重在问题解决上。 (4)结果管理与过程管理相统一,重在结果管理上。 (5)管理所追求得公平与效率相统一,重在公平上。 (6)公共组织得外部管理与内部管理相统一,重在外部管理上。 (7)服务管理与管制管理相统一,重在服务上。 (8)管理制度与技术相统一,重在制度创新上。 2、简要说明市场经济国家政府得主要职能。 第一,建立并维护社会与市场秩序。 第二,提供公共物品及基础服务。 第三,调控宏观经济并保持稳定。 第四,进行收入与财产得再分配。 第五,保护自然资源与环境。 3、非政府公共组织得基本特征与作用就是什么？ 非政府公共组织得基本特征就是(1)非政府性(2)公益性(3)正规性(4)专门性(5)志愿性。作用:由于非政府公共组织沟通了政府与社会各方面得联系,架起了政府与社会之间联系得桥梁与纽带,因此非政府公共组织发挥着双重性、广泛性、针对性、中介性、公益性得作用。 二、论述题 1、论述政府失效理论得主要内容及其给我们得启示。 答:政府失效理论得主要内容:政府失效也称政府失灵,就是指政府主体机制等方面有在本质上得缺陷,而无法使资源配置得效率达到最佳得情景。这一理论对人得假设,包括政府公务员,都就是经济人假设。由此,这一理论认为在政治决策过程中,人得一切行为都可以瞧成就是经济行为。政府行政过程中得目得肯定就是
增进公共利益得判断得到质疑。政府失效主要就是现在公共政策得失效;公共物品供给得低效率;内部性与政府扩张性; “寻租”及腐败。 政府失效理论给我们得启示主要有以下三点: 1)单纯依靠市场与过多依靠市场政府干预都就是行不通得,必须两者互相制约、协调才能促进市场得健康发展。 2)必须明确界定政府管理得范围、权限,同时积极培育建立社会主义市场,并不断完善社会主义市场经济体制,使市场自身而不就是靠政府去发挥作用。 3) 在进行经济改革得同时也必须进行政治体制改革,只有这样才能保证济体制改革得顺利进行。 4) 加强各项法律、法规得建设,使政府得决策过程与管理过程都能纳入正常得监督系统或机制之中。 2、结合实际谈谈转型时期我国政府得职能应如何转变。 答:所谓政府职能转换并不就是简单得加强或削减政府得干预范围或力度,而就是指在市场经济体制下政府得工作内容、工作重点、工作方式要有重要得改变。转型期我国政府职能得转换主要表现在以下几个方面:1、改变管理念,为全社会提供服务。2、改革企业制度,实现政企分开。3、加强法制建设,形成公平竞争得市场经济体系。4、实行宏观调控,稳定经济发展。5、加强政府自身建设,提高工作效率。 综合以上政府工作内容、重心得转移,我们可以用简单得四句话概括政府职能转化得特点,即:政府工作由全面转向适度;由微观转向宏观;由直接转向间接;由人治转向法治。例如:多年来,在计划经济得影响下,无论就是各级政府机关、企事业单位、还就是平民百姓都以文件为依据,即所谓得红头文件。在今天发展社会主义市场经济得条件下,就显现出不稳定、随意性等一系列得问题与局限性。我们过去曾经将市场经济与计划经济严重对立起来,否定了市场经济对促进生产力所起得重要作用,阻碍了社会经济得发展,因此我们必须大力发展市场经济,尤其在竞争充分得领域更要充分发挥市场经济得调节作用,积极利用这支“瞧不见得手”,与此同时也要大力加强法制建设,以保证市场经济得健康发展。 公共管理学作业2 一、简答题:
钢琴考级1到10级曲目 第一级 一基本练习 (一)C 大调(二)G 大调(三)F 大调 二技巧性练习曲 （一）旋律与伴奏练习曲（No13)车尔尼曲 （二）练习曲（No60) 拜厄曲 （三）练习曲尼古拉耶夫曲 三中国乐曲 （一）小白菜（二）玩具（三）扎红头绳 四外国乐曲 （一）乡村快步舞曲（二）摇摆的印地安人（三）春之歌 第二级一基本练习 （一）D大调（二）A大调（三）E大调 二技巧性练习曲 （一）练习曲车尔尼曲 （二）练习曲车尔尼曲 （三）五声音阶旋律（小宇宙第二册）巴托克曲 三中国乐曲 （一）二月里来（二）熊猫（三）两只老虎 四外国乐曲 （一）G 大调苏格兰舞曲（二）女神之舞（三）柔板 第三级 一基本练习 （一）C大调与a 小调（二）G大调与e 小调 （三）D大调与b 小调（四）A大调与#f 小调 （五）E大调与#c 小调（六）B大调与#g 小调 二技巧性练习曲 （一）双手交替练习曲车尔尼曲 （二）练习曲莱蒙曲 （三）练习曲格季克曲 三复调性乐曲 （一）康定情歌（二）布列舞曲（三）小赋格 四乐曲 （一）郊游（二）舞曲（三）小诙谐曲
第四级 一基本练习 （一）F大调d 小调（二）bB大调g 小调 （三）bE大调c 小调（四）bA大调f 小调 （五）bD大调bB小调（五）bG大调bE小调 二技巧性练习 （一）练习曲T.拉克曲 （二）练习曲车尔尼曲 （三）练习曲莱蒙曲 三复调性乐曲 （一）打莲湘（二）小广板（三）小步舞曲（选自第二法国组曲第四首）巴赫曲 四乐曲 （一）云雀之歌（二）回旋曲（三）森林波尔卡（四）八音盒 第五级 一基本练习 本级基本练习的范围共六组，调性分组与第三级完全一样，只是变成了双手同向四个八度。从本级开始有最低速度要求，每分钟最漫要达到７６拍。请注意琶音与音阶同样速度，都是１６分音符，都是每拍四个音。 二技巧性练习曲 （一）练习曲车尔尼曲（二）断奏练习曲（三）陀螺 三复调性乐曲 （一）二部创意曲（二）前奏曲（三）听妈妈讲那过去的事情 四乐曲 （一）C 大调小奏鸣曲第一乐章（二）＜巴蜀之画＞选曲 （三）D 大调小奏鸣曲第二乐章（四）圣诞老人 第六级 一基本练习 本级基本练习范围共六组,调性分组与第四级完全一样,只是扩展为双手同向四个八度.本级最低速度84。请注意琶音与音阶同样速度,都是16分音符,都是每拍四个音。 二技巧性练习曲 (一)半音阶练习曲车尔尼曲 (二)练习曲车尔尼曲 (三)分解琶音练习曲杜维诺依曲 三复调性乐曲 (一)布列舞曲(选自<第二英国组曲>) 巴赫曲 (二)赋格<喜悦> 丁善德曲 (三)二部创意曲巴赫曲 四乐曲 （一）第二小奏鸣曲第一乐章巴赫曲
. 公共管理学 作业1 1、公共管理的主体是公共组织，客体是公共事务，目的是实现公共利益， 公共管理过程是公共权力的运作过程。 2、公共物品或服务是指具有效用的不可分割性、消费的非竞争性和受益的 非排他性等特性的产品。 3、公共管理学是一门研究公共管理活动规律的学科，它是在公共行政学的 基础上发展起来的。 4、一般来讲，政府的职能应分为两部分：政治职能和管理职能。 5、政府职能的演变大致经历了限制政府干预、主张政府干预和对政府职能 的重新思考三个阶段。 6、非政府公共组织的基本特征是：非政府性、公益性、正规性、专门性和 志愿性。 7、我国非政府公共组织的构成主要包括：社会团体和民办非企业单位。 8、目前我国非政府公共组织的主要活动领域有：环境保护、扶贫救困、社会公益等方面。其具有双重性、广泛性、针对性、中介性的公益性特点。 9、公共管理者主要是指政府官员、政府公职人员和非政府公共组织的管理 人员。其职业具有鲜明的特点，主
要表现在执行公共权力、服务公共社会两个方面。 10、当代公共管理者必备的职业能力主要包括管理认知能力、管理诊断能专业资料． . 力、管理决策能力和人际沟通能力四个方面。 二简答题 1、公共管理与企业管理有何区别？、1⑴目的不同，公共管理是公益性的，企业管理的目的是盈利； ⑵限制因素不同，公共管理整个过程受到法律的限制，企业管理的根本原动力是追求高额利润，经济气候是企业管理的主要影响因素，法律在其活动中仅是一个外部制约因素； ⑶物质基础不同，公共管理所需要的各种物质资源主要来自于税收和发行债券，其经费预算属于公共财政支出，必须公开化，接受纳税人的监督，企业所需的各种物质资源主要来自投资的回报即利润，其管理所需的物质资源是自主的，不需要公开化； ⑷管理人员选拔方式不同，公共管理人员是由专门的部门或机构相对独立地考核、评估，主要考虑其政治才干和倾向，公共管理人员有职业化、终身化的趋向，企业管理人员根据其处理特定事务的能力被聘用； ⑸绩效评估的指标不同，评估公共管理成效的主要指标是行为的合法性、公众舆论的好坏、各种冲突的减少程度、公共项目的实施与效果、公共产品的数量及消耗程度，偏重于社会效益，企业管理绩效的主要指标是销售额、净收益率、生产
钢琴一到十级的考试曲目 一级 一、基本练习（抽查其中一组）本级练习的范围有三组：（1）、C 大调（2）、G 大调（3）、F 大调每组内容有：1、音阶：大调音阶、一个八度，双手同向；2、琶音：分解主三和弦短琶音，三个音为一组；3、和弦：主三和弦的原位及转位。 二、练习曲1、练习曲No88、 三、奏鸣曲1、G 大调小奏鸣曲四乐曲1、在花园里2、划船拜厄阿特伍德 玛依卡帕尔汤普森 二级 一、基本练习（抽查其中一组）本级练习的范围有三组：（1）、D 大调（2）、 A 大调（3）、E 大调每组内容有：1、音阶：大调音阶、两个八度，双手同向；2、琶音：分解主三和弦短琶音，两个八度，双手同向，本级短琶音分为A、B 两种，考生自选一种3、和弦：主三和弦的原位及转位。 二、练习曲1、练习曲op599 三、复调1、、小步舞曲 四、奏鸣曲1、C大调小奏鸣曲，第二乐章op57、No1 五、乐曲1、天真烂漫车尔尼巴赫比尔布格缪勒 三级 一、基本练习（抽查其中一组）本级基本练习的范围有六组：（1）、 C 大调与a小调（2）、G大调与e小调（3）、大调与b小调（4）、A大调与#f小调（5）、E大调与#c 小调（6）、B大调与#g小调每组内容有：1、音阶：大调及其关系和声小调音阶，三个八度，双手同向2、琶音：分解主三和弦琶音，三个八度，双手同向 二、练习曲1、练习曲op37 三、复调1、加伏特舞曲 四、奏鸣曲1、 F 大调小奏鸣曲0P168 第一乐章 五、乐曲1、第一次丧失op68 莱蒙巴赫迪亚贝利舒曼四级 一、基本练习（抽查其中一组）本级基本练习的范围有六组：（1）、F 大调与d小调（2）、bB大调与g小调（3）、bE大调与c小调（4）、bA大调与f小调（5）、bD大调与 b 小调（6）、bG大调与 e 小调每组内容有：1、音阶：大调及其关系和声小调音阶，三个八度，双手同向1、琶音：分解主三和弦琶音，三个八度，双手同向 二、练习曲1、练习曲op718 三、复调1、G 大调前奏曲 四、奏鸣曲1、、G 大调小奏鸣曲op20 第一章 五、乐曲1、、孩子们的舞蹈车尔尼亨德尔杜舍克桑桐五级 一、基本练习（抽查其中一组）本级基本练习的范围有六组：（1）、 C 大调与a小调（2）、G大调与e小调（3）、D大调与c小调（4）、A大调与#f 小调（5）、E大调与#c小调（6）、B大调与#g 小调每组内容有：1、音阶：大调及其关系和声小调音阶，三个八度，双手同向2、琶音：分解主和弦琶音，三个八
《公共管理学》形成性考核作业 《公共管理学》作业一 简答题 1、简述构成公共组织的基本要素。 构成公共组织的基本要素就是:组织人员、物质因素、组织目标、职能范围、机构设置、职位设置、权责分配、规章制度、 2、简述公共组织设计的原则。 答:(1)职能目标原则;(2)完整统一原则;(3)精干效能原则;(4)法制原则;(5)职、权、责一致原则;(6)人本原则、 3、简述人力资源管理的基本职能。 答:人力资源管理的基本职能就是:(1)人力资源的获取(规划、录用与选拔);(2)人力资源的发展(整合培训、职业发展、管理发展、组织发展);(3)人力资源的激励(联结报酬与绩效、工作再设计、提升工作的满足感、绩效评估);(4)人力资源的维持(人际关系与沟通问题、员工福利问题、工作环境问题、职业安全问题);(5)人力资源的研究(政策、规则、技术、方法)、 《公共管理学》作业二 简答题 1、简述公共财政的职能。 答:(一)资源配置的职能:1、为全社会提供公共物品与公共服务; 2、矫正外部效应;3、对不完全竞争的干预;(二)调节收入分配的职能:1、经济公平:强调投入与收入的对称(等价交换、按劳分配);2、社会公平:将收入差距维持在现阶段社会各个阶层居民所能接受的合理范围内(调节贫富差距);(三)稳定经济职能:1、充分就业;2、物价稳定;3、国际收支平衡、 2、简述现代公共部门人力资源管理制度的基本精神。 答:人力资源管理理论的基本精神就是:第一,确定以人为中心的管理思想;第二,把组织瞧作整体,不仅开发“力的资源”,而且开始走向开发组织、整体的“心的资源”,注重整体效益、群体目标、团队精神;第三,在管理原则上既强调个人又强调集体;第四,在管理方法上既强调理性又强调情感;第五,在领导方式上既强调权威又强调民主;第六,在管理实践中既强调能力也重视资历。 《公共管理学》作业三 论述题 1、谈谈您对组织变革的动力与阻力的认识。 组织改革的动力 (一)组织改革的外部动力 首先,适应市场经济体制就是组织改革最深层的动力。改革的本质动力就是经济体制的改革与市场化的驱动,改革的目的与任务就是适应经济发展的需求与要求。目前我国正处于市场经济体制逐步完善,市场经济迅速发展的关键时期,政府作为市场宏观调控的主体,为了更好地履行宏观调配职能,促进经济的平稳快速发展,必然要先对自身的职能与机构进行改革。其次,政治体制改革就是行政改革的直接动力。中国的战略改革系统不仅包括经济体制改革也包括政治体制改革,作为上层建筑的政治体制必须与经济体制改革的深入同时展开。目前,我国的政治体制改革还处于观念与理论研讨阶段,并没有与经济体制改革相适应,可以说就是暂落后于经济体制改革。行政改革作为政治体制改革的重要方面,其改革必将带动政治体制改革的发展,这对我国的政治改革的深入起到积极的促进作用。
基本练习： 1.音阶（分手、两个八度） 2.分解和弦（三个音一组、分手）c、g、d大调，a、e和声小调 曲目： a组 1.练习曲（op.599 no.19）……车尔尼 2.巴斯皮耶……亨德尔 3.忧伤……巴托克 4俄罗斯民歌……贝多芬 b组: 1.练习曲……贝尔科维奇 2.德国民歌……巴赫 3.奏鸣曲（g大调第四乐章）……海顿 4.诉说……古里特 选曲： 1.浏阳河……唐碧光作曲、陈静斋改编 2.田园曲（op.100）……布格缪勒 3.儿童游戏……巴托克 第二级 基本练习： 1.音阶（分手、两个八度） 2.分解和弦（四个音一级、分手）c、g、d、a、f大调，a、e、d和声小调 曲目： a组： 1.练习曲……古里特 2.加沃特舞曲……亨德尔 3.回旋曲……莫扎特 4.旋律……舒曼 b组： 1.练习曲（op.176 no.14）……杜威诺阿 2.加沃特舞曲……库普兰 3.快板……阿尔诺尔德 4.儿童献花舞……金爱平 选曲： 1.天真烂漫（op.100）……布格缪勒 2.苏格兰舞曲……贝多芬 3.爵士小练习……赛贝尔
基本练习： 1.音阶（分手、三个八度） 2.琶音（分手、两个八度） 3.半音阶（分手） c、g、 d、a、 e、b、f大调，a、e、b、d、g、c和声小调 曲目： a组 1.练习曲……勒士豪恩 2.波罗涅兹舞曲……巴赫 3.急板（op.* no.1）……库劳c大调小奏鸣曲第2乐章c大调小奏鸣曲第3乐章 4.叙事曲（op.100）……布格缪勒 b组 1.练习曲（op.37）……雷蒙 2.库朗特舞曲……亨德尔 3.快板（op.36 no.3）……克列门蒂 4.勇敢的骑士……舒曼 选曲： 1.手摇风琴……肖邦塔科维奇 2.歌曲……泰勒曼 3.甜密的幻想……柴科夫斯基 第四级 基本练习： 1.音阶（合手、四个八度） 2.琶音（合手、四个八度） 3.半音阶（合手、两个八度） c、g、 d、a、 e、b、 f、bb、be大调及其关系和声小调 曲目： a组 1.练习曲（op.46 no.1）……海勒 2.阿勒曼德舞曲……巴赫 3.回旋曲（op.36 no.5）……克列门蒂g大调小奏鸣曲第3乐章g大调小奏鸣曲第2乐章 4.老祖母的小步舞曲……格里格 b组 1. 练习曲（op.849 no.12）……车尔尼 2. 二部创意曲（no.4）……巴赫 3. 回旋曲（op.20 no.1）……杜赛克
权威钢琴考级曲目一、全国钢琴考级曲目一级 一、基本练习 1 C大调 2 G大调 3 F大调 二、技巧性练习曲 1 《旋律与伴奏练习曲》（Op.823,No.13)车尔尼曲 2 《拜厄钢琴基本教程》第60首 3 《练习曲》尼古拉耶夫曲 三、中国乐曲 1 《小白菜》龚耀年改编 2 《玩具》李重光曲 3 《扎红头绳》王震亚编曲 四、外国乐曲 1 《乡村快步舞曲》 2 《摇摆的印第安人》吉洛克曲 3 《春之歌》汤普森曲 全国钢琴考级曲目二级 一、基本练习 1 D大调 2 A大调 3 E大调 二、技巧性练习曲 1 《练习曲》(Op.599No.59) 车尔尼曲
2 《练习曲》(Op.139No.19) 车尔尼曲 3 《声音阶旋律》（小宇宙第二册）巴托克曲 三、中国乐曲 1 《二月里来》五震亚编曲 2 《熊猫》黎英海曲 3 《两只老虎》林成进改编 四、外国乐曲 1 《G大调苏格兰舞曲》（Op.38.No.23）黑斯勒曲 2 《女神之舞》蓬基耶利曲 3 《柔板》斯坦别尔特 全国钢琴考级曲目三级 一、基本练习 1 C大调与a小调 2 G大调与e 小调 3 D大调与b小调 4 A大调与升f小调 5 E大调与升c小调 6 B大调与升g小调 二、技巧性练习曲 1 《双手交替练习曲》(Op.139No98) 车尔尼曲 2 《练习曲》(Op.37No.10) 莱蒙曲 3 《练习曲》(Op.32No.19) 格季克曲 三、复调性乐曲 1 《康定情歌》陈鸿铎改编 2 《布列舞曲》巴赫曲
3 《小赋格》齐波里曲 四、乐曲 1 《郊游》路珈改编 2 《舞曲》（Op.27,No.17）卡巴列夫斯基曲 3 《小诙谐曲》（Op.3,No.3）谢列凡诺夫曲 4 《F大调小奏鸣曲第一乐章》贝多芬曲 全国钢琴考级曲目四级 一、基本练习 1 F大调d 小调 2 bB大调g 小调 3 bE大调c 小调 4 bA大调f 小调 5 bD大调bB小调 6 bG大调bE小调 二、技巧性练习 1 《练习曲》(Op.172No.4) T.拉克曲 2 《练习曲》(Op.453No.55) 车尔尼曲 3 《练习曲》(Op.37No.42) 莱蒙曲 三、复调性乐曲 1 《打莲湘》陈铭志曲 2 《小广板》D，斯卡拉蒂曲 3 《小步舞曲》（选自第二法国组曲第四首）巴赫曲 四、乐曲 1 《云雀之歌》(0p，39。No，22)柴科夫斯基曲 2 《回旋曲》(0p，151，No，1)狄亚贝里曲
1．第1题 新公共管理范式建立的学科基础为（）。 A.政治学 B.行政学 C.经济学 D.行政法学 您的答案：C 2．第2题 1、新公共管理范式产生于（）。 A.19世纪60年代末70年代初 B.19世纪70年代末80年代初 C.20世纪60年代末70年代初 D.20世纪70年代末80年代初 您的答案：D 3．第3题 新公共管理运动肇始于（）。 A.英国 B.美国 C.德国 D.新西兰 您的答案：A 4．第4题 在交易费用、产权契约安排和资源配置效率之间建立起内在的联系，从而成为沟通交易费用理论与产权理论桥梁的是（）。 A.彼德原理 B.科斯定理 C.阿罗不可能性定理 D.墨菲法则 您的答案：B 5．第5题 新公共管理运动肇始于（）。 A.英国 B.美国 C.德国 D.新西兰 您的答案：A 6．第6题 公共选择理论实际上提出的是一种（）。 A.政府万能理论 B.政府失败理论 C.市场万能理论 D.市场失败理论 您的答案：B 7．第7题 在私人部门里，战略思想演变阶段中的战略规划阶段的特征为 A.通过努力做到与预算相符，寻求更好的运营控制 B.通过预测下一年度以后的情况，寻求更有效的成长规划 C.通过战略性思考，寻求对市场和竞争能力作出更快反应 D.管理所有资源，寻求竞争优势，取得未来的成功 您的答案：A 此题得分：0.0
8．第8题 目标管理的理论和方法的创立者是美国管理学家（）。 A.彼得？杜拉克C.泰勒 B.帕金森D.法约尔 您的答案：C 此题得分：0.0 9．第9题 政府运用供应这个手段，所针对的对象是 A.公共产品 B.私人产品 C.半公共产品 D.半私人产品 您的答案：A 10．第10题 在交易费用、产权契约安排和资源配置效率之间建立起内在的联系，从而成为沟通交易费用理论与产权理论桥梁的是 A.彼德原理 B.科斯定理 C.阿罗不可能性定理 D.墨菲法则 您的答案：B 11．第11题在私人部门中，组织的最终目标为（）。 A.追求可持续经济利润的最大化 B.追求可持续政治利益的最大化 C.追求社会公平 D.追求公众的满意度 您的答案：A 12．第12题 1、新公共管理范式产生于（）。 A.19世纪60年代末70年代初 B.19世纪70年代末80年代初 C.20世纪60年代末70年代初 D.20世纪70年代末80年代初 您的答案：D 13．第13题 对非政府公共组织也可称作（）。 A.第一部门 B.第二部门 C.第三部门 D.公共组织 您的答案：C 14．第14题 关于绩效管理对于新公共管理范式的价值，以下说法不正确的是（）。 A.绩效管理与市场模式相统一 B.绩效评价与管理是分权化改革的迫切要求
公共管理学习题 一、简答题 1、公共管理的内涵: 所谓公共管理, 就是公共组织运用所拥有的公共权力, 为有效地实现公共利益, 对社会公共事务进行管理的社会活动。主要包括以下几点: ( 1) 公共管理的主体是公共组织( 2) 公共管理的客体是社会公共事务( 3) 公共管理的目的是实现公共利益( 4) 公共管理的过程是公共权利的运作过程 2、政府职能演变经过的阶段: ( 1) 限制政府干预( 2) 主张政府干预( 3) 对政府职能的重新思考 3、简述政府失效理论的基本观点及政府失效的表现: 政府失效理论的基本观点是对人的”经济人”的假设。即认为人是自利的、理性的, 而且每个人都在追求个人利益的最大化, 政府公务员也不例外。由此看来, 在政治决策过程中, 人的一切行为都可看成是经济行为, 而使”政府政治过程的目的肯定是增进公共利益的假设”受到质疑而不得不被放弃。( 1) 公共政策失效 ( 2) 公共产品供给的低效率( 3) 内部性与政府扩张( 4) ”寻租”及腐败 4、简述非政府公共组织的基本特征: ( 1) 非政府性( 2) 公益性( 3) 正规性( 4) 专门性( 5) 志愿性 5、公共政策的特征表现在哪些方面: ( 1) 公共性( 2) 利益选择性( 3) 目标指向性( 4) 权威约束性 ( 5) 功能多极性( 6) 动态稳定性 6、简述公共政策规划的主体和基本原则: 公共政策规划的主体是指参与政策方案设计与研究的所有机构和人员。 ( 1) 执政党( 2) 立法机关( 3) 行政机关( 4) 利益集团( 5) 大众传媒 政策规划的原则是指政策规划需要遵循的基本准则: ( 1) 公正原则( 2) 受益原则
第三项内容是复调性乐曲一共有三首，自选一首。 第一首《二部创意曲》（）巴赫曲 这首二部创意曲在原来的考级中也有，因为它非常经典，所以，在这次的新版本教材中还是选用了。 首先，巴赫作品的处理还是要跟大家强调一下，由于这些作品的原谱上是很少有什么（除音符以外）标记的，所以，这个版本中的标记仅供大家参考，不限制各位教师和考生的音乐理解和个性发挥，只要是符合巴赫风格的处理，都是允许的。 这首作品，我们选用了一种很有精神、生动的处理，以做参考。主题是跳音和连音组合，而且，每次主题出现的时候都要保持相同的很精神、生动的性质。 根据乐谱上的标记，八分音符是断奏，要弹得干净利落；十六分音符相对来说连一些，手指积极主动，但不能弹得很连很粘，其实，是一种很颗粒的非连奏。对主题的处理，大家要特别注意处理最高音位置的八分音符“F”，不能和后面的十六分音符连着弹，而是要分开。这在后面主题多次出现的地方也要统一处理好。 第4到7小节这种音型弹奏的时候要强调节奏的点，每四个音把第一个音稍加强调。第5和6小节两只手同时的地方，要靠这个节奏点把两只手对齐，不能四个音都重。 这首曲子有一些很难的句子，要独拿出来仔细练习。比如，第10小节，右手的位置比较开张弹奏的时候手臂要用转动的动作，手掌和手指不能松懈，要有架子感，手掌像跷跷板一样左右转动。 类似的还有第19至20小节，右手又与第15小节类同。 大家还可以看到，这些部分十六分音符的地方有的加了跳音记号。但是，这种跳音不是要跳起来，而是要弹得干脆、颗粒、不拖泥带水，而且音点很清楚，就已达到跳的效果了，不能因为弹奏跳音把手抬得很高，那样的话不但弹不出好的声音，还会因为离键过高而没有把握性。这种跳音如果弹得明亮、干净，会显出其中的旋律性，是很好听的。 这首作品作为二个声部的创意曲，大家一定要按照上面的原则先分手弹奏得很熟练，很清楚，节奏很统一了，再两只手合起来弹。 第二首《前奏曲》凯列尔曲 这是巴洛克时期的一首前奏曲，复调性很强，有着类似建筑物的那种结构形式感。 这首作品的主题性质是挺拔、神气的。一开始，右手、左手的主题隔两拍相继出现，交叉在一起，像建筑一样，有一种很平衡的感觉，两只手合在一起形式感很强。另外，交叉在一起的主题还出现了两遍，第一遍是mf，第二遍是mp，所以，均衡的感觉和明暗的对比就更加明显了。 大家可以想象建筑的话，是高低错落、有明有暗的，这首作品很多地方都出现了对比，所以大家要仔细地做出来。尤其是强弱对比的地方，要弹奏出“阶梯力度”的层次与对比，巴罗克时期，有两排键盘的古钢琴，在一排上弹出了mf,另一排上弹出mp. 像第6小节的地方也可以做出一个强、一个弱。 在第10小节右手的第一拍，从前面的一拍四个音的十六分音符，变为一拍六个音的三连音，大家弹奏的时候要特别注意，保持节奏和速度的统一性。 下面具体对装饰音进行一下说明。
政策评估的（ B ）反映的是政策的效率和效能标准。 A.稳定标准 B.事实标准 C.价值标准 D.成本标准 公共政策的权威性来源于它的（B ）。 A.合理性 B.合法性 C.操作性 D.强制性 以下哪项不是常见的政策手段？（ D ）。 A.行政手段 B.经济手段 C.思想政治手段 D.文化手段 我国的社会团体具有“半官半民”的特点，说的是其组织的（ B ）。 A.广泛性 B.双重性 C.针对性 D.中介性 非政府公共组织的基本特征有（ CD ）。 A.公益性 B.正规性 C.专门性 D.志愿性 公共管理者的职业能力主要包括（ ABCD ）方面的能力。 A.管理认知能力 B.管理诊断能力 C.管理决策能力 D.人际沟通能力 ）（ A 。，在1776年撰写《国富论》论述了对政府角色理解的学者是 A.亚当·斯密 B.凯恩斯胡德C. D.史蒂文·科恩 ）界定政府职能的主要依据是（ 3 A.财政赤字商品服务质量下降 B. 市场失灵 C. D.政府干预 公共管理学是一门研究（ C ）的学科 A.公共决策 B.公共组织维护 C.公共管理活动规律
D.公共环境 （ C ）是由公共政策制定主体的本质特点决定，也是其阶级性的反映。 A.目标指向性 B.权威约束性 C.功能多极性 D.利益选择性 公共政策具有（ ABCD ）等特征。 A.公共性 B.利益的选择性 C.权威的约束性 D.功能的多极性 本来应当由政府承担的职能，却因没有尽到职责而出现了“真空”现象，我们称其为政府职能的（ A ）。 A.缺位 B.越位 C.错位 D.不到位 公共管理者主要是指（ ACD ）。 A.政府官员 B.企业领导 C.政府公职人员 D.非政府公共组织的管理人员 我国在计划经济体制下，政府对社会和经济实施全面的干预，是一个（B ）。 A.小政府 B.全能的政府 C.间接的政府 D.恰当的政府 政府失效的主要表现及原因有（ABCD ）。 A.公共政策失效 B.公共物品供给的低效率 C.内部性与政府扩张 寻租及腐败D. 现代公共管理是以（ B ）为核心的、多元化的开放主体体系。 A.企业 B.政府 C.文化团体 D.研究机构
声乐：中央音乐学院钢琴考级七级曲目指导 来源：歌词大全 https://www.doczj.com/doc/d95579454.html, 七级A组（1）练习曲车尔尼 此曲时十七世纪音乐风格得乐曲。练习时要求颗粒性强，弹性要好，手指转换的地方手臂要放松，转弯的动作要正确，保持严谨的节奏律动。此外还要注意左手根音的写法：第一、三行中左手强调保留四、五指，第二行左手改为跳动的低音写法，在看谱例时要特别认真的分清左手根音中八分音符，二分音符的长度，以便于更好完成低音级进向下的音阶旋律线条，确保旋律的趣味性，另外结尾时要做大的渐弱。 七级A组（2）三部创意趣巴赫 练习时注意巴洛克时期巴赫的古典风格特点，此曲旋律线不长，每一音符做为一个单位，要求弹奏得有弹性、活泼。声音上弹得不要太重，保持乐曲得流动性。手指触动琴键要把音断开一些弹奏，如用连奏会感觉跟此曲风格不贴切。第一行第三小节得三十二分音符弹得不要太快，要保持全篇三十二分音符和十六分音符得统一性，保证稳定得节奏律动。第五十二页第四行第一小节的左右手旋律互换，如果感觉两手交叉弹奏比较困难，也可以两手互换弹奏。内心感觉是上面的旋律交叉发展下去和下面的旋律交叉发展上来。三十二小节的延长音要保持住，时值要够，不能短促，以确保从容进入尾声。 七级A组（3）回旋曲莫扎特（bB大调奏鸣曲第三乐章）此曲是轮舞式舞蹈的性质，主题多次重复出现的古典作品。在两个主题之间插入一个不同主题的插部，当主题之间插入一个不同主题的插部，当主题出现时要回到原来主题的风格上去。插部（五十三页最后一小节）则在音乐形象上形成一个不同风格的对比段落出现，节奏上要保持统一的节奏律动。音乐形象上的不同表现在于主题比较轻盈、有弹性、力度上弹奏得要轻（p）。插部表现出比较浑厚、雄浑、有力地（f）音量对比。
公共管理学作业 选择题 1 . (3分) 下面哪一项不是西方新公共治理的差不多理念？（C） A.政府的职能是“掌舵”而不“划浆” B.引进私营部门的治理手段和体会 C.公务员保持政治中立 D.公共服务以顾客为导向 2 . (3分) 公共治理与企业治理有（ABCD）等方面的差别。 A.限制因素不同 B.物质基础不同 C.治理人员选拔方式不同 D.绩效评估不同 3 . (3分) 在进行政策规划时，具体问题具体分析，实事求是地认识阻碍政策规划的环境因素，灵活客观地选择规划方案，是（C）原则的表达。 A.优化原则 B.变化原则 C.权变原则 D.系统原则 4 . (3分) 依照公共政策对社会有关群体的阻碍来分，公共政策可分为（AB）等 A.分配性政策 B.调剂性政策 C.元政策 D.差不多政策 5 . (3分)
以下属于公共政策制定的间接主体的是（B）。 A.政党 B.智囊专家 C.立法机关 D.行政机关 6 . (3分) 公共治理者要紧是指（ACD）。 A.政府官员 B.企业领导 C.政府公职人员 D.非政府公共组织的治理人员 7 . (3分) 界定政府职能的要紧依据是（C） A.财政赤字 B.商品服务质量下降 C.市场失灵 D.政府干预 8 . (3分) 公共治理者的职业能力要紧包括（ABC）方面的能力。 A.治理认知能力 B.治理诊断能力 C.治理决策能力 D.人际沟通能力 9 . (3分) 目前我国非政府公共组织的要紧活动领域有（ABD）等方面。 A.环境爱护 B.扶贫救困 C.公共基础设施的提供 D.社会公益 10 . (3分)
非政府公共组织的差不多特点有（ABCD）。 A.公益性 B.正规性 C.专门性 D.理想性 第2 大题 简答题 1 . (10分) 转型期我国政府职能的定位表达在哪些方面？答：转型期我国政府职能的定位表达在以下几方面： 1、强化公共服务，保证公共产品的供给。 2、强化社会治理，保证社会公平、公平。 3、实现宏观调控，稳固经济进展。 4、加强政府自身建设，提高公共服务质量。 2 . (10分) 公共政策规划的差不多程序包括哪几个步骤？答：公共政策规划的差不多程序包括以下几个步骤： 1、确立政策目标。 2、拟订政策方案。 3、评估政策方案。
全国钢琴演奏考级作品集新编第一版曲目讲解第十级（上） 第十级一共有四项内容。在乐曲分组上，第十级和第八九级是一样的，分别是“基本练习”、“技巧性练习曲”、“巴洛克——古典风格乐曲”和“浪漫——近现代风格乐曲”。 第一项内容是基本练习。 第十级的基本练习一共有六组，包括了从一个降号到六个降号的大小调音阶和琶音，是六组“降号调”。弹奏时音阶和琶音需要向与反向相结合。 和第七级、第八级相比，第九级和第十级取消了属七和弦琶音和减七和弦琶音，但音阶和琶音扩展为同向和反向的结合以及增加了两只手四个音大和弦的练习。在弹奏同向反向音阶和琶音之前，可以找一下规律：音阶和琶音的跨度是四个八度，上行的前两个八度是同向，到中间时双手开始反向，回中间后，两只手再同向上行两个八度，从高点下来两个八度到中间之后，反向两个八度，回到中间之后再共同向下行。找到规律后就不会太难了。希望大家在准备第九级的阶段中，都把同向与反向练得非常熟练。 另外，第九级、第十级和第一级、第二级有相呼应之处，是增加了主和弦的考核。第一级、二级时曾练过小和弦；到第九级、十级就该练大和弦了。因为在高的级别中会遇到较多大和弦类的技术，在基本练习中练了主要的大和弦，知道基本的弹奏方法，对作品的演奏会有很大的好处。 大和弦的弹奏方法和要领与演奏小和弦在主要方面是一样的。弹奏时身体要挺拔，上身可略前倾，以协调使用身体的力量。全身和全手臂的力量都要协调用到，手指在弹奏的瞬间可以“抓”一下，把四个音同时抓到一起，使之声音集中。由于弹和弦的时候下键很快，给了键盘一个作用力，键盘也就有一个反作用力，传回手臂，因此，在和弦发生的同时，手肘要略放开一点儿，以释放反作用力，使声音具有弹性。在这个瞬间肘关节往外的动作，开始练习时可以夸张一些，以体会力量的通畅和反作用力的释放，等熟练以后就要使动作逐步简练和自然，只需要保留很小的手肘动作，起到减震作用即可。因为弹和弦时，经常会出现的问题是把反作用力，压回键盘，造成声音没有弹性而发不出来；也有学生把反作用力顶回肩膀，既难看且声音难听。另外，弹和弦时，手不要离键过远过高，触键的位置要靠近键盘一点儿为好，尤其手不是特别大的学生，靠近键盘一点儿弹比较牢靠，过高容易出现敲击的动作和声音。除了弹奏和弦的要领以外，指法也要很清楚，1、2、5指以外的音用3指还是4指，要根据音的距离而定。同时，此时暂不用的手指不要碰键，不出杂音，音响才能比较干净。 主和弦是用二分音符写成，每音两拍，可用相同的速度弹奏。 减去了大调属七和弦琶音和小调减七和弦琶音，增加的是双手四个音一起的大和弦转位进行（具体弹法可参阅第九级中的相关说明）。不过在第十级中速度要求更加提高了一点，是每分钟126拍，而且所有音阶和琶音都是用十六分音符写成，要同速弹奏。在考试的时候，不能低于这个速度。 第二项内容是技巧性练习曲，一共三首，自选一首。 第一首《练习曲“博士”》（选自《儿童园地》）德彪西曲 这首曲子选自德彪西的《儿童园地》。德彪西的《儿童园地》是由六首曲子组成的一个组曲，是德彪西为自己的女儿写的。其中的第一首《练习曲“博士”》，描绘了小孩子们整天练琴练得十分枯燥，好像“克列门蒂”都弹成“博士”了，当然这不是真的博士，而是带有嘲讽意味的。曲子开头是模仿克列门蒂《名手之道》的练习曲方式来写的。但是德彪西写得很有意思，他把规整的织体变出好多花样，好像小孩在弹这首曲子的时候，弹着弹着就想入非非，开始重复发挥自己的想象力了，把练习曲弹出这样那样的变化，像玩儿似的非常高兴，越发挥弹得越兴奋。所以，相比于一些较刻板的练习曲而言，这首乐曲完全是一个艺术品。