Gossamer supercoductivity and the mean field approximation of a new effective Hubbard model
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成都2024年统编版小学六年级上册英语自测题(含答案)考试时间:80分钟(总分:140)B卷考试人:_________题号一二三四五总分得分一、综合题(共计100题共100分)1. 填空题:A rabbit's ears are very ______ (长).2. 选择题:What is the name of the popular movie genre that involves superheroes?A. DramaB. ComedyC. ActionD. Adventure答案: C3. 听力题:I like to eat ________ for breakfast.4. 选择题:How many legs does a dog have?A. 2B. 3C. 4D. 55. 填空题:My favorite activity is to ________ (参加派对).6. 填空题:I have a _____ (便当盒) for my lunch at school.我有一个便当盒,装我在学校的午餐。
7. 选择题:What is the name of the famous explorer who discovered America?A. ColumbusB. MagellanC. Vasco da GamaD. Cook8. (19) States has 50 states. 填空题:The ____9. 填空题:I love visiting toy museums to see rare and ________ (形容词) toys.10. 填空题:The ______ (鸭子) quacks when it swims.11. 选择题:What is the opposite of 'hot'?A. WarmB. ColdC. BoilingD. Burning答案:B12. 听力题:The dog is _____ under the table. (sleeping)13. 小鹦鹉) mimics my voice. 填空题:The ___14. 填空题:A kitten purrs when it is ______ (开心).15. 填空题:In my family, my grandma likes to be called .(在我的家庭中,我的奶奶喜欢被称为。
周深三体主题曲英文The Three-Body Problem Theme SongVerse 1:The universe is spinning, a deadly gameMysteries unfold and the truth is revealedBlack holes and stars come into playThe war of the three worlds begins today Chorus:We will unlock the secrets of the three-body problem And see what the future has in storeForces of nature, driving science forwardThe power of technology at our fingertipsVerse 2:From afar we watch the chaos unfoldAs humanity searches for answers untoldA complex equation that none can solveWe must harness the power of the stars above Chorus:We will unlock the secrets of the three-body problem And see what the future has in storeForces of nature, driving science forwardThe power of technology at our fingertips Bridge:We must learn the mysteries of the cosmosIf we want to survive against all oddsA race against time to save all mankindThis is the ultimate challenge of our time Chorus:We will unlock the secrets of the three-body problemAnd see what the future has in storeForces of nature, driving science forwardThe power of technology at our fingertipsThrough our minds and collective knowledge, we can work together to solve the three-body problem and discover the secrets of the universe. Only then will we be able to understand our place in this vast cosmos.。
the damned human race课文The Damned Human Race可恶的人类Mark Twain马克•吐温I have been studying the traits and dispositions of the “lower animals,”and contrasting them with the traits and dispositions of man. I find the result humiliating to me. For it obliges me to renounce my allegiance to the Darwinian theory of the Ascent of Man from the Lower Animals and to name it the Descent of Man from the Higher Animals.我一直在研究“低级动物”的特点和性情,并将其与人的特点和性情相比较。
我发现其结果令我羞愧难当,因为它迫使我宣布不再忠信达尔文“人是从低级动物进化而来”的理论,而将其更名为“人是从高级动物退化而来的”。
In proceeding toward this unpleasant conclusion I have not guessed or speculated or conjectured, but have used what is commonly called the scientific method. That is to say, I have subjected every postulate that presented itself to the crucial test of actual experiment, and have adopted it or rejected it according to the result. These experiments were made in the London Zoological Gardens, and covered many months ofpainstaking and fatiguing work.在得出这一令人不快的结论的过程中,我没有进行猜测、推断或者揣测,而是运用了人们通常所说的科学方法。
三体的英文作文题英文:As a huge fan of the Three-Body Problem, I have always been fascinated by the depth and complexity of the story. The way Liu Cixin weaves together science fiction, history, and philosophy is truly remarkable. The characters are so well-developed and the plot is so engaging that I find myself completely immersed in the world of the novel every time I pick it up.One of the things that I love most about the Three-Body Problem is the way it explores the concept of human nature and the implications of our actions. The novel presents a bleak and dystopian vision of the future, where humanity is faced with an existential crisis. It raises thought-provoking questions about the nature of progress and the consequences of our technological advancements.The Three-Body Problem also delves into the idea ofcommunication and the challenges of understanding an alien civilization. The concept of the Trisolarans and their unique way of thinking is both fascinating and terrifying. It really makes you wonder about the possibilities of extraterrestrial life and the potential for communication with beings from other worlds.In addition to its thought-provoking themes, the Three-Body Problem is also just a really thrilling and entertaining read. The way the story unfolds, with its twists and turns, keeps me on the edge of my seat every time. The sense of wonder and awe that the novel evokes is truly something special.Overall, the Three-Body Problem is a masterpiece of science fiction that has had a profound impact on me. It has sparked countless conversations and debates among my friends and I, and I am constantly recommending it to anyone who will listen. It's a book that stays with you long after you've finished it, and I know that I will continue to revisit it for years to come.中文:作为《三体》的忠实粉丝,我一直对这个故事的深度和复杂性深感着迷。
库里历史三分王英语作文Title: The Reign of Stephen Curry: A Historic Journey to Three-Point SupremacyStephen Curry, the epitome of shooting excellence, has etched his name in the annals of basketball history as the undisputed three-point king. His remarkable journey from a relatively unheralded prospect to a global icon is atestament to his unparalleled skill, dedication, and resilience.Born on March 14, 1988, in Akron, Ohio, Curry wasdestined for greatness. Raised in a basketball-centric family, with his father Dell Curry being a former NBA sharpshooter, Stephen inherited not only the genes but also the passion for the game. Despite his diminutive stature, Curry possessed an innate shooting touch that would revolutionize the way basketball is played.Curry's collegiate career at Davidson College served as a precursor to his impending stardom. His electrifying performances and deep range shooting captivated audiences nationwide, leading Davidson to unprecedented success in the NCAA tournament. It was during these formative years that Curry honed his craft, mastering the art of the three-point shot with unparalleled precision.In 2009, Curry declared for the NBA draft and was selected by the Golden State Warriors with the seventhoverall pick. Little did the league know that they were witnessing the rise of a generational talent who would redefine the boundaries of long-range shooting. From the moment he stepped foot on an NBA court, Curry's impact was immediate and profound.The 2012-2013 season marked the beginning of Curry's ascent to superstardom. His lethal combination of handles, shooting prowess, and court vision mesmerized fans andconfounded defenders. With each game, Curry seemed to shatter records and push the boundaries of what was deemed possible. His ability to drain three-pointers from distances that were previously unimaginable left spectators in awe and opponents in despair.The pinnacle of Curry's career came during the 2015-2016 NBA season. In a campaign that can only be described as transcendent, Curry led the Warriors to an unprecedented 73-9 regular-season record, eclipsing the legendary mark set by the 1995-1996 Chicago Bulls. Along the way, he shattered his own record for most three-pointers made in a single season, cementing his status as the greatest shooter of all time.Curry's impact extends far beyond the basketball court. Through his philanthropic endeavors and unwavering commitment to social justice causes, he has become a role model for millions around the world. His influence transcends bordersand boundaries, inspiring a new generation of athletes to dream big and work tirelessly to achieve their goals.As we reflect on Curry's historic journey to three-point supremacy, one thing is abundantly clear: his legacy is secure. With multiple MVP awards, NBA championships, and an unparalleled impact on the game, Stephen Curry has earned his place among the all-time greats. And yet, knowing his relentless work ethic and insatiable desire for improvement, it's safe to say that the best may still be yet to come.。
小学下册英语第3单元真题(含答案)考试时间:90分钟(总分:100)B卷一、综合题(共计100题共100分)1. 选择题:What type of animal is a parrot?A. MammalB. FishC. ReptileD. Bird答案: D2. 听力题:The Earth's atmosphere protects us from harmful ______.3. 选择题:What is the term for a young cassowary?a. Chickb. Calfc. Kitd. Pup答案:a4. 填空题:I love to read ______ (故事书) that spark my imagination.5. 听力题:The scientific study of matter and its changes is called _____.6. War was a period of tension between the USA and the ______ (苏联). 填空题:The Cold7. 填空题:The __________ (历史的动力) often comes from change.8. 选择题:What do you call a book with pictures and stories for children?A. NovelB. DictionaryC. ComicD. Magazine答案:C9. 填空题:My sister has a _____ that she carries everywhere.10. 填空题:The ________ was a pivotal event in the history of civil rights.11. 听力题:The man has a funny ________.12. 填空题:A frog can survive in both ______ (水) and on land.13. 选择题:What is the largest land animal?A. GiraffeB. RhinoC. ElephantD. Hippo14. 听力题:I enjoy ________ at the beach.15. 听力题:I can ________ (lead) a team effectively.16. 选择题:What do you call a young sea lion?A. PupB. CalfC. KitD. Cub17. 填空题:The bird has bright _______ (鸟有鲜艳的_______).18. 填空题:The __________ Desert is one of the largest deserts in the world. (撒哈拉)19. 填空题:I like to ______ (与朋友一起) play games.I found a ________ on the ground.21. 听力题:I enjoy ______ with my friends. (talking)22. 选择题:What is the largest mammal in the ocean?A. SharkB. WhaleC. DolphinD. Seal答案:B23. 选择题:What is the name of the famous American singer known as the "Queen of Soul"?A. Aretha FranklinB. Whitney HoustonC. Tina TurnerD. Diana Ross答案: A24. 填空题:The _______ (The Cuban Revolution) led to a communist government in Cuba.25. 听力题:The _______ of a plant can be very long.26. 听力题:A ____ is a small creature that enjoys digging tunnels underground.27. 选择题:How many colors are in the flag of the USA?A. TwoB. ThreeC. FourD. Five28. 听力题:My ______ loves to travel and take photos.29. 填空题:My sister is a good __________. (学生)30. 听力题:The _____ (自行车) is fast.What do we call the place where animals are kept for public viewing?A. FarmB. ZooC. AquariumD. Circus答案:B32. 选择题:What do we call the large body of fresh water?A. OceanB. RiverC. LakeD. Sea答案:C33. 听力题:I see my friends at __________.34. 选择题:What is 5 x 2?A. 8B. 9C. 10D. 1135. 选择题:What color is a typical fire truck?A. BlueB. GreenC. RedD. Yellow答案:C36. 选择题:What do we call the structure that connects two points over water?A. TunnelB. BridgeC. HighwayD. Road37. 听力题:The chemical formula for myristic acid is ______.38. 听力题:A __________ is a large area of flat land with few trees.39. ic sank on its maiden voyage in ________ (1912). 填空题:The Tita40. 选择题:What do you call a collection of stars?A. GalaxyB. PlanetC. CometD. Asteroid41. 填空题:The ladybug is good for the _________. (花园)42. 选择题:What is the name of the famous ancient city in Italy?A. PompeiiB. FlorenceC. RomeD. Venice答案: A43. 选择题:What is the capital of Portugal?A. LisbonB. MadridC. ParisD. Rome44. 选择题:What is the name of the sweet food made from sugar and flour?A. CandyB. CookieC. CakeD. Pie答案: B45. 选择题:What is the opposite of lazy?A. ActiveB. EnergeticC. DiligentD. All of the above答案:D46. 填空题:The ______ (果汁) of fruits is refreshing to drink.She is a great ________.48. 填空题:I have a toy _____ that moves with a remote.49. 填空题:My favorite ice cream flavor is ________ (巧克力).50. 填空题:The _______ (小犀牛) has thick skin and is very strong.51. 填空题:The skunk is known for its strong ________________ (气味).52. 填空题:A ____(community garden) fosters local cooperation.53. 选择题:What is the name of the famous battle fought in 1815?A. Battle of GettysburgB. Battle of WaterlooC. Battle of HastingsD. Battle of Agincourt答案: B54. 选择题:What is the smallest continent?A. AfricaB. AsiaC. AustraliaD. Europe55. 选择题:What is the name of the highest waterfall in the world?A. Niagara FallsB. Angel FallsC. Victoria FallsD. Iguazu Falls答案:B56. 填空题:The __________ (奴隶制度) was abolished in the 19th century.My sister enjoys __________ (交流).58. 填空题:I enjoy learning about different ______ (语言) and cultures.59. 选择题:What is 20 15?A. 3B. 4C. 5D. 6答案: C60. 填空题:A ______ (植物的多样性) initiative can help biodiversity.61. 听力题:A chameleon can change its ______.62. 选择题:What is the primary color of the sky on a clear day?A. RedB. BlueC. GreenD. Yellow答案:B63. 听力题:The ________ (mountain) is covered in snow.64. 听力题:My cousin is a ______. She loves to run.65. 填空题:We have a ______ (丰富的) library collection.66. 听力题:The Earth's crust is primarily made up of minerals that contain ______.67. 填空题:__________ (实验室安全培训) is crucial for preventing accidents.68. 填空题:The owl hoots at ________________ (夜晚).__________ are often used in fireworks for colorful displays.70. 填空题:The crab scuttles across the _________. (沙滩)71. 填空题:I enjoy visiting the ______ (图书馆) to read and borrow books.72. 听力题:We need to _____ (buy/sell) more fruits.73. 选择题:What is the sweetest fruit?A. LemonB. BananaC. StrawberryD. Grapefruit74. 选择题:Which country is known for the Eiffel Tower?A. ItalyB. FranceC. SpainD. Germany答案:B75. 填空题:The _____ (种子库) preserves genetic diversity.76. 填空题:The __________ (历史的传承) connects us to the past.77. 选择题:What is the name of the famous American author known for "The Adventures of Tom Sawyer"?A. Mark TwainB. Ernest HemingwayC. F. Scott FitzgeraldD. John Steinbeck答案: A78. 听力题:I ride my bike to ___ (school/home).A _______ can symbolize peace and renewal.80. 填空题:My pet bird loves to _______ (飞翔) around the room.81. 选择题:What do you call a large body of water surrounded by land?A. LakeB. OceanC. RiverD. Stream答案:A82. 听力题:The term "endothermic" refers to a reaction that _______ heat.83. 填空题:_____ (evergreen) trees stay green all year round.84. 听力题:A __________ is a large area of grasslands.85. 填空题:The ________ was a famous historical figure in India.86. ims landed at Plymouth Rock in ______ (1620年). 填空题:The Pyra87. 填空题:A deer uses its keen sense of smell to detect ________________ (危险).88. 听力题:The symbol for strontium is _____.89. 听力题:The city of Baghdad is the capital of _______.90. 选择题:What do we call the study of plants?A. BiologyB. BotanyC. ZoologyD. Ecology答案: BWhat is the chemical symbol for carbon?A. CB. CaC. CoD. Cl答案: A. C92. 填空题:I like to collect __________ (玩具名) from different __________ (国家).93. 选择题:What is the main ingredient in pizza dough?A. RiceB. FlourC. SugarD. Salt答案: B. Flour94. 选择题:What is the closest galaxy to the Milky Way?A. AndromedaB. TriangulumC. WhirlpoolD. Sombrero95. 听力题:The chemical symbol for iodine is ______.96. 听力题:My uncle is a talented ____ (actor).97. 听力题:The cat steals a ______ from the table.98. 选择题:How many continents are there in total?A. FiveB. SixC. SevenD. Eight99. 填空题:My grandfather tells __________ (有趣的) jokes.100. 填空题:When I feel _______ (情感), I like to listen to _______ (音乐类型). It makes me feel better.。
英语问答知识点总结1. What is the capital of France?The capital of France is Paris.2. Who was the first president of the United States?The first president of the United States was George Washington. 3. What is the tallest mountain in the world?Mount Everest is the tallest mountain in the world.4. Who wrote the play "Romeo and Juliet"?William Shakespeare wrote the play "Romeo and Juliet".5. What is the chemical symbol for water?The chemical symbol for water is H2O.6. Who discovered the theory of relativity?Albert Einstein discovered the theory of relativity.7. What is the largest planet in our solar system?Jupiter is the largest planet in our solar system.8. Who painted the Mona Lisa?Leonardo da Vinci painted the Mona Lisa.9. What are the primary colors?The primary colors are red, blue, and yellow.10. What is the capital of Australia?The capital of Australia is Canberra.11. Who was the first astronaut to walk on the moon?Neil Armstrong was the first astronaut to walk on the moon.12. What is the formula for calculating the area of a rectangle? The formula for calculating the area of a rectangle is length x width.13. What is the boiling point of water in Celsius?The boiling point of water in Celsius is 100 degrees.14. Who wrote "To Kill a Mockingbird"?Harper Lee wrote "To Kill a Mockingbird".15. What is the capital of China?The capital of China is Beijing.16. Who was the first woman to win a Nobel Prize?Marie Curie was the first woman to win a Nobel Prize.17. What is the largest ocean in the world?The largest ocean in the world is the Pacific Ocean.18. Who invented the light bulb?Thomas Edison invented the light bulb.19. What is the currency of Japan?The currency of Japan is the yen.20. Who painted the Starry Night?Vincent van Gogh painted the Starry Night.21. What are the three branches of the US government?The three branches of the US government are the executive, legislative, and judicial branches.22. What is the chemical symbol for gold?The chemical symbol for gold is Au.23. Who wrote the play "Hamlet"?William Shakespeare wrote the play "Hamlet".24. What is the largest desert in the world?The largest desert in the world is the Sahara Desert.25. Who is known as the father of modern physics?Albert Einstein is known as the father of modern physics.26. What are the primary colors of light?The primary colors of light are red, green, and blue.27. Who was the first woman to fly solo across the Atlantic Ocean? Amelia Earhart was the first woman to fly solo across the Atlantic Ocean.28. What is the capital of Brazil?The capital of Brazil is Brasília.29. Who wrote the novel "1984"?George Orwell wrote the novel "1984".30. What is the chemical symbol for oxygen?The chemical symbol for oxygen is O.31. Who painted the Sistine Chapel ceiling?Michelangelo painted the Sistine Chapel ceiling.32. What is the largest river in the world?The largest river in the world is the Amazon River.33. Who discovered penicillin?Alexander Fleming discovered penicillin.34. What is the currency of Russia?The currency of Russia is the ruble.35. Who wrote the novel "Pride and Prejudice"?Jane Austen wrote the novel "Pride and Prejudice".36. What is the capital of South Africa?The capital of South Africa is Pretoria.37. Who was the first person to set foot on the South Pole?Roald Amundsen was the first person to set foot on the South Pole. 38. What is the chemical symbol for carbon?The chemical symbol for carbon is C.39. Who painted the Last Supper?Leonardo da Vinci painted the Last Supper.40. What is the largest continent in the world?The largest continent in the world is Asia.41. Who developed the theory of evolution by natural selection?Charles Darwin developed the theory of evolution by natural selection.42. What is the capital of Italy?The capital of Italy is Rome.43. Who wrote the play "Macbeth"?William Shakespeare wrote the play "Macbeth".44. What is the chemical symbol for iron?The chemical symbol for iron is Fe.45. Who painted the Creation of Adam?Michelangelo painted the Creation of Adam.46. What is the longest river in the United States?The longest river in the United States is the Missouri River.47. Who discovered the structure of DNA?James Watson and Francis Crick discovered the structure of DNA.48. What is the currency of Mexico?The currency of Mexico is the peso.49. Who wrote the novel "Moby-Dick"?Herman Melville wrote the novel "Moby-Dick".50. What is the largest sea in the world?The largest sea in the world is the Philippine Sea.In conclusion, these are some important and interesting knowledge points that everyone should know. Whether it's geography, history, science, or literature, knowing these facts canhelp us understand the world around us and appreciate the accomplishments of humanity. Keep learning and growing, and never stop seeking knowledge!。
小学下册英语第1单元期末试卷英语试题一、综合题(本题有50小题,每小题1分,共100分.每小题不选、错误,均不给分)1 I enjoy playing ______ at the park.2 What do we call a collection of books?A. LibraryB. BibliographyC. AnthologyD. Archive答案: A. Library3 What do you call a large body of saltwater?A. LakeB. SeaC. OceanD. River答案:C4 Hydrogen ions give acids their ________ properties.5 A ______ is a type of bond formed by sharing electrons.6 I always take ______ to school.7 The capital of India is __________.8 I have a toy _______ that can do tricks.9 The elephant's ears help to regulate its ________________ (体温).10 I like to ride my ______.11 The __________ (历史的传承价值) shape identities.12 My dad is a great ____ (storyteller).13 What is the main topic of a story called?A. CharacterB. SettingC. PlotD. Theme答案:D14 We will go _____ (shopping/working) tomorrow.15 What is the capital of Australia?A. SydneyB. MelbourneC. CanberraD. Brisbane答案:C16 What color do you get when you mix red and white?A. PinkB. PurpleC. OrangeD. Brown17 Listen and number.听录音,给下面的图片标出正确的顺序。
极限特工3终极回归主题曲歌词导读:All the Way Up (Remix)- Fat Joe / French Montana / InfaRed / Remy Ma / David Guetta / Glowinthedark(电影《极限特工:终极回归》预告片插曲)Nothing can stop me I'm all the way up我势不可挡,我旗开得胜All the way up势不可挡I'm all the way up我势不可挡I'm all the way up我无人能敌Nothing can stop me I'm all the way up我无人能挡,我旗开得胜Shorty what you want shorty what you need妹子你要干嘛你想干嘛My niggas run the game we ain't ever leavin'我们主宰一切从未失势Countin' up this money we ain't never sleepin'数不完的钱彻夜狂欢You got v12 I got 12 v's你有引擎我却有豪车Got bottles got weed got molly觥筹交错烟雾萦绕妹子相伴I'm all the way up我无人能及Shorty what you want I got what you need 妹子你想要什么我就有什么Nothing can stop me I'm all the way up我无人能挡无人能敌Nothing can stop me I'm all the way up我无人能挡无人能敌All the way up无人能及I'm all the way up我无人能及I'm all the way up我无人能敌Nothing can stop me I'm all the way up我无人能挡,我旗开得胜Just left the big house to a bigger house房子越换越大Ain't have a girlfriend but the bitch is out我没有女友只有进进出出的妹子Chanel croc bag shit ain't even out想要香奈儿鳄鱼包却还没发售With the gold chains himalayan birkin' cocaine脖带着金链手夹比尔克香烟Lit it up pac shit I hit 'em up抽着香烟我就是焦点I'm talkin' color money purple yen and blue dirham 我有各色各样的钱紫色日元蓝色摩洛哥币I got brown lira I ain't talkin' 'bout ross bitch 我有棕色发的里拉不是上次的罗斯I'm that nigga on viagra dick我精力旺盛That means I'm all the way up我意思是我无人能挡Shorty what you want I got what you need妹子你想要什么我就有什么I'm all the way up我无人能及Nothing can stop me I'm all the way up我无人能挡,我旗开得胜Nothing can stop me I'm all the way up我无人能挡,我高高在上Nothing can stop me I'm all the way up我无人能挡,我无法企及Nothing can stop me I'm all the way up我无人能挡,我众生相拥【极限特工3终极回归主题曲歌词】1.《极限特工3:终极回归》观后感「精选」2.2017电影《极限特工:终极回归》观后感3.动作片《极限特工:终极回归》观后感「精选」4.热血经典《极限特工3:终极回归》观后感5.《极限特工:终极回归》观后感6.好莱坞大片《极限特工3:终极回归》观后感7.2017最刺激的好莱坞影片《极限特工3:终极回归》观后感8.前任3主题曲《说散就散》歌词上文是关于极限特工3终极回归主题曲歌词,感谢您的阅读,希望对您有帮助,谢谢。
a r X i v :c o n d -m a t /0211131v 2 [c o n d -m a t .s u p r -c o n ] 8 N o v 2002Gossamer supercoductivity and the mean field approximation of a new effectiveHubbard modelYue YuInstitute of Theoretical Physics,Chinese Academy of Sciences,P.O.Box 2735,Beijing 100080,China(February 1,2008)We construct a new effective two-dimensional Hubbard model by taking the different electron occupancy on site into account.The mean field state of the new Hamiltonian gives rise to the gossamer superconducting state proposed by Laughlin recently [1].PACS numbers:74.20.-z,74.20.Mn,72.-h,71.10.FdSince the high temperature superconductor of Cu-O cuprate was discovered,the mechanism of the supercon-ductivity has been attracting much research interesting due to various unusual properties of the high T c supercon-ductor.A well-known model trying to describe the nor-mal state properties is the 2-dimensional Hubbard model or t-J model [2,3].Many analytical and numerical inves-tigations on these two models have been carried out [4].Anderson proposed a resonant valence bond (RVB)state as a mean field state of the models to explain the undoped cuprate as a Mott insulator while the superconductor is thought as a doped Mott insulator [5].Although many progresses have been made along the clues of the Hub-bard model and t-J model,there is no persuasive evidence that the theory of the high T c superconductivity of the cuprates can firmly based on these two models and var-ious extended models of them.Especially,the quantum antiferromagnetic state may always be favorable in these two-dimensional models for a small doping.In a recent work,Laughlin proposed a new scenario for the high T c superconducting cuprate,called the gossamer superconductivity [1].The basic notion is that,instead of the full projection in the RVB state,which forbits the double-occupancy of electrons on a site,a partial projec-tion acting on a BCS-type wave function is introduced.If the partial projection is not far from the full projec-tion,one has a very tiny superfluid density.This is called the gossamer ughlin’s explicit mi-croscopic wave function for the gossamer superconductor reads|ΨG =i(1−αn i ↑n i ↓)|ΨBCS ,(1)|ΨBCS =k(u k +v k c †k ↑c †−k ↓|0 ,where c †k σis the Fourier component of the electron cre-ation operator c †iσon a two-dimensional lattice;n iσ=c †iσc iσis the electron number operator at site i .The pro-jection operator Πα= i (1−αn i ↑n i ↓)for 0≤α≤1is the partial Gutzwiller projection which has an inverse Π−1α= i (1+βn i ↑n i ↓)if α<1and β=α/(1−α).The BCS superconducting state |ΨBCS is defined as usual byu 2k =1E k),v 2k =1E k),(2)u k v k =∆kξ2k +∆2kfor the elec-tron dispersion ǫk ,chemical potential µand the super-conducting gap ∆k .It has been pointed out that the state |ΨG may be superconducting even at half filling.Furthermore,Laughlin has found that the state |ΨG is the exact ground state of the model HamiltonianH G =kE k ˜b †k σ˜b k σ,(3)where ˜b k σ=Παb k σΠ−1for b k ↑=u k c k ↑+v k c −k ↓andb k ↓=u kc k ↓−v k c −k ↑annihilate the BCS state.Explic-itly,˜b k σreads ˜b k ↑=1N je i k ·r j[u k (1+βn j ↓)c j ↑+v k (1−αn j ↑)c †j ↓],˜b k ↓=1N je i k ·r j[u k (1+βn j ↑)c j ↓−v k (1−αn j ↓)c †j ↑].(4)Laughlin has shown that for any magnitude of α,the quasiparticle energies remain at E k ,which indicates the psuedogap phenomenon.Right following up Laughlin’s work,Zhang has checked the gossamer superconductivity in a more realistic effective Hubbard model [6].It was found that the gossamer superconducting state is simi-lar to the RVB superconducting state,except that the chemical potential is approximately pinned at the mid of the two Hubbard bands away from the half filling.Ref.[6]indicated that the gossamer superconducting state may possibly be a good variational state of the effec-tive Hubbard model.Nevertheless,it is still in question to make an explicit relation between the Hamiltonian (3)and that of the effective Hubbard model used in ref.[6].In this paper,we try to provide a new effective Hub-bard model which is the extension of the Hubbard model and t-J model.Our extending method is other than all the previous extended models of those two models.We consider the case that the lattice sites are allowed to be1double-occupied by electrons with opposite spins.Be-cause of the on-site Coulomb repulsion between electrons,the electrons hopping between sites becomes dependent on the occupancy of sites.There are three possible hop-ping processes that may have different hopping probabil-ities (see,Fig.1).On the other hand,when electrons are paired,the coupling between pairs may also be de-pendent on the the occupancy of the sites (Fig.2)while the hopping may be dependent on the paring gap.What is new by employing such a new effective Hubbard model is that the Laughlin gossamer superconducting state may be viewed as the mean field state of this ly,there is a gossamer superconducting phase in the system described by this new effective Hubbard Hamiltonian.To extend the Hubbard model,we first write down the Hamiltonian of the effective Hubbard modelH eh =− i =j ;σ(t ij c †iσc jσ+h.c )+Uin i ↑n i ↓−µi,σn iσ+i =jJ ij (S i ·S j −12c †στσσ′c σ′is the local spin operator.One canrewrite this Hamiltonian asH eh =− i =j ;σ(t ij c †iσc jσ+h.c )−1Nk ǫk e i k ·(r i −r j ).Notice that the chemical po-tential and the gap-dependence,we can estimate δ(a )t ij byt (1)ij =αNk[a 2ξk +b 2(E k −ξk )]e i k ·(r i −r j ),where the coefficients a l and b l ,in principle,depend onU and J ij but we are unable to calculate them at present.We leave them to be determined later.The α-dependence in eq.(8)is because in the limit U →0,α→0while the hopping probability becomes independent of the site-occupancy.The coupling between the pairing operators ˆDij and ˆD †ijmay also dependent on the occupancy of the sites i and j (See Fig.2):ˆJ ij =J ij +J (1)ij(n i +n j )+J (2)ij n i n j ,(9)whereJ (1)ij =A 1αJ ij ,J (2)ij =A 2α2J ij ,(10)with the undetermined coefficients A l .The extended ef-fective Hubbard model we are considering is given byH eff=− i =j ;σ(ˆt ij,σc †iσc jσ+h.c )−12i =jˆ∆†ij ˆD ij−12α2,b 2=−α2+β22Nk[(β−α)E k +(β+α)ξk ],µG =1whereˆt Gij,σ=k E k2(v2k−u2k)−(αv2k+βu2k)n i¯σ+1Nu k v k e i k·(r i−r j)×(1+(α+β)n i¯σ+αβn i¯σn jσ). Substituting the definition(4)of˜b kσinto the gossamer superconducting Hamiltonian(3),one can directly check that the gossamer superconducting Hamiltonian(3)is exactly the same as the meanfield Hamiltonian(15),i.e.,H G MF=H G.(17) Thus,wefind that the gossamer superconducting state is indeed afixed point of the system described by the effec-tive Hubbard model(11).If the parameters of the hop-ping,exchange,chemical potential and interaction are not far from theirfixed point values,the system may exhibit a gossamer superconductity.In conclusions,we have constructed a new effective Hubbard model in which the different hopping proba-bilities and the pairing couplings are introduced due to the different site-occupancy at sites.We showed that there is a superconducting phase in such a system since the meanfield Hamiltonian of this system in a proper choice of the parameters is just the gossamer supercon-ducting Hamiltonian.Beside the superconducting phase, this new effective Hubbard model is anticipated to have a fruitful phase structure.In ref.[6],it was shown that there is a critical interaction strong U c that separates the gossamer superconducting phase from the Mott insultor phase.In this new effective Hubbard model,we see that even the superconducting gap vanishes or the superfluid density is completely suppressed(α=1),the dispersion of electron as well as the interaction between electrons for the latter are dependent on the occupancy of the site that electrons lying on.We expect these unusual behaviors of the electrons may cause unusual normal state properties and relate to the anomalous features in the cuprates.It is possible that the phase diagram of this model may have a better overlap to the cuprate superconductors.The further works are in progress.The author is grateful to useful discussions with Shao-jin Qin,Tao Xiang and Lu Yu.He would like to thank Shiping Feng for him to draw the author’s attention to gossamer superconductivity.This work was partially supported by the NSF of China.(c)(b)(a)jjjji iiiji ji(c)(b)(a)jjjjiii iijji。