Slave Particle Studies of the Electron Momentum Distribution

The electron momentum distribution function in the $t-J$ model is studied in the framework of slave particle approach. Within the decoupling scheme used in the gauge field and related theories, we treat formally phase and amplitude fluctuations as well as

arXiv:cond-mat/9304011v1 8 Apr 1993SlaveParticleStudiesoftheElectronMomentumDistributionintheLowDimensionalt JModelShipingFeng ,1J.B.Wu,2Z.B.Su,1,2andL.Yu1,21International2InstituteCentreforTheoreticalPhysics,P.O.Box586,34100Trieste,ItalyofTheoreticalPhysics,ChineseAcademyofSciences,Beijing100080,ChinaTheelectronmomentumdistributionfunctioninthet Jmodelisstudiedintheframeworkofslaveparticleapproach.Withinthedecouplingschemeusedinthegauge eldandrelatedtheories,wetreatformallyphaseandamplitude uctuationsaswellasconstraintswithoutfurtherapproximations.Ourresultindicatesthatthe

electronFermisurfaceobservedinthehigh-resolutionangle-resolvedphotoemissionandinversephotoemissionexperimentscannotbeexplainedwithinthisframework,andthesumruleforthephysicalelectronisnotobeyed.Acorrectscalingbehavioroftheelectronmomentumdistributionfunctionneark～kFandk～3kFinonedimensioncanbereproducedbyconsideringthenonlocalstring elds[Z.Y.Wengetal.,Phys.Rev.B45,7850(1992)],buttheoverallmomentumdistributionisstillnotcorrect,atleastatthemean eldlevel.

PACSnumbers:71.45.-d,75.10.Jm

The electron momentum distribution function in the $t-J$ model is studied in the framework of slave particle approach. Within the decoupling scheme used in the gauge field and related theories, we treat formally phase and amplitude fluctuations as well as

I.INTRODUCTION

Thet Jmodelisoneofthesimplestmodelscontainingtheessenceofstrongcorrelationsanditsimplicationsforoxidesuperconductivity[1,2]stillremainanoutstandingproblem.Thet Jmodelwasoriginallyintroducedasane ectiveHamiltonianoftheHubbardmodelinthestrongcouplingregime,wheretheon-siteCoulombrepulsionUisverylargeascomparedwiththeelectronhoppingenergyt,andthereforetheelectronsbecomestronglycorrelatedtoavoidthedoubleoccupancy.Inthiscase,theelectron’sHilbertspaceisseverelyrestrictedduetothisconstraint σ CiσCiσ≤1.Anderson[1]andlaterZhangandRice[2]havearguedstronglythatthebasicphysicsofoxidesuperconductorscanbedescribedbythet Jmodel.

Thenormalstatepropertiesofoxidesuperconductorsexhibitanumberofanomalouspropertiesinthesensethattheydonot tintheconventionalFermiliquidtheory[3,4].SomepropertiescanbeinterpretedonlyintermsofadopedMottinsulator[3,4].Acentralquestioninthetheoryofthesestronglycorrelatedsystemsconcernsthenatureoftheelec-tronFermisurface(EFS)[4].Thehigh-resolutionangle-resolvedphotoemissionandinversephotoemissionexperiments[5]demonstratetheexistenceofalargeEFS,withanareacon-sistentwiththebandstructurecalculations.SincethebandtheoryisconsistentwiththeLuttingertheorem[6],thismeansthattheEFSareacontains1-δelectronpersite,whereδistheholedopingconcentration.AlthoughthetopologyofEFSisingeneralagreementwithone-electron-bandcalculations,theFermivelocityisquitedi erent.Thisindicatesthatelectroncorrelationsrenormalizeconsiderablytheresultsobtainedintheframeworkofasingle-particletreatment.Ithasrecentlybeenshownbysmallclusterdiagonalizationthatinatwo-dimensional(2D)squarelatticetheEFSwithinthet JmodelisconsistentwithLuttinger’stheorem[7].MonteCarlosimulationsforanearlyhalf- lled2DHubbardmodelalsosupportthisresult[8].Moreover,theelectronmomentumdistributionfunctionofa2Dt Jmodelwasstudied[9]byusingtheLuttinger-Jastrow-Gutzwillervariational

The electron momentum distribution function in the $t-J$ model is studied in the framework of slave particle approach. Within the decoupling scheme used in the gauge field and related theories, we treat formally phase and amplitude fluctuations as well as

Fermiedge.Forone-dimensional(1D)largeUlimitHubbardmodelwhichisequivalenttothet Jmodel,OgataandShiba[10]obtainedtheelectronmomentumdistributionfunc-tionbyusingLieb-Wu’sexactwavefunction[11].TheirresultalsoshowstheexistenceofEFSaswellasthesingularbehavioratk～kFandk～3kFinthemomentumdistributionfunction.Furthermore,YokoyamaandOgata[12]studiedthe1Dt Jmodelbyusingexactdiagonalizationofsmallsystemsandfoundthepower-lawsingularityappearingatkFinthemomentumdistributionfunction.

Sofar,strongcorrelatione ectscanbeproperlytakenintoaccountonlybynumericalmethods[7–10,12],suchasvariationalMonte-Carlotechnique[13],exactclusterdiagonaliza-tion[14],andvariousrealizationsofquantumMonte-Carlomethod[15].Apartfromthesenumericaltechniques,ananalyticalapproachtothet Jmodelreceivingagreatdealofattentionistheslaveparticletheory[4,16],wheretheelectronoperatorCiσispresentedas

Ciσ=a ifiσwithaiastheslavebosonandfiσasthefermion,orviceversa.Thiswaythe

non-holonomicconstraint

σ CiσCiσ≤1(1)

isconvertedintoaholonomicone

a iai+ σ fiσfiσ=1,(2)

whichmeansagivensitecannotbeoccupiedbymorethanoneparticle.Anewgaugedegreeoffreedommustbeintroducedtoincorporatetheconstraint,whichmeansthattheslaveparticlerepresentationshouldbeinvariantunderalocalgaugetransformationai→aieiθ(ri,t),fiσ→fiσeiθ(ri,t),andallphysicalquantitiesshouldbeinvariantwithrespecttothistransformation.Wecallsuchslaveparticleapproachas”conventional”.Theadvantageofthisformalismisthatthechargeandspindegreesoffreedomofelectronmaybeseparatedatthemean eldlevel,wheretheelementarychargeandspinexcitationsarecalledholons

The electron momentum distribution function in the $t-J$ model is studied in the framework of slave particle approach. Within the decoupling scheme used in the gauge field and related theories, we treat formally phase and amplitude fluctuations as well as

uidsofspinonsandholonsrepresentthesamesetofelectrons,andtheymust,onaverage, owtogether.ThedecouplingofchargeandspindegreesoffreedominthelargeUlimitHubbardmodelisundoubtedlycorrectin1D[10],wherethechargedegreesoffreedomofthegroundstateareexpressedasaSlaterdeterminantofspinlessfermions,whileitsspindegreesof …… 此处隐藏：6181字，全部文档内容请下载后查看。喜欢就下载吧 ……