Chern-Simons theory of QFH

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1、Chern-SimonsTheoryofFractionalQuantumHallEectKalinVetsigianMay7,2001AbstractTheFractionalQuantumHalleectisreviewedfromtheperspectiveofChern-Simonseldtheory.Theinteracting2Delectrongasinmagneticeldproblemisexactlymappedtoabosonicprobleminwhichtheboso

2、nscoupletoanewgaugeeldinadditiontotheelectromagneticeld.ItisshownthatmeaneldanalysisinthenewformulationissucienttoexplainallbasicfeaturesofthefractionalquantumHalleect.1IntroductionThetheoryofFractionalQuantumHallEect(FQHE)providesuswithastrik-ing

3、exampleofastronglyinteractingsystemwhichcanbewellunderstoodintermsoftheweakinteractionsofnontrivialeectiveobjects.WhatismoststrikingaboutFQHEisthatduetotheirfractionalchargetheeectiveobjects,unlikeatomsandmolecules,cannotbethoughtofasasimplecollection

4、ofmoreelementaryparticles.TheFQHEisbasicallytheproblemofinteractingelectronsin2Dinthepres-enceofastrongperpendicularmagneticeld.Thegroundstatewavefunctioniscompletelydierentfromthenon-interactingoneandtheproblemcannotbeunderstoodbymeansofperturbationt

5、heorystartingfromthenon-interactingcase.ThemanybodygroundstatewavefunctionwasguessedbyLaughlinwiththehelpofthevariationalprinciple.Oncethishighlynon-trivialstepwasmadethefractionalHalleecttheorydevelopedquicklyandmanydierentwaysoflookingattheproblemwe

6、reinvented.InthispaperwewillreviewaworkdonebyZhang,HanssonandKivelson[1][2]whomappedtheinteractingelectronproblemtooneofinteractingbosonscoupledtoanadditionalgaugeeld.Theadvantageofthenewformulationisthatnearllingfactorsoftheform1/(2k+1)theessentialfe

7、aturesofFQHEcanbederivedbyastraightforwardmeaneldanalysis.Thisformulationenablesustocomputequantitiesinasystematicallyimprovablewayusingthemachineryofperturbationtheory.Chern-SimonsLandau-Ginzburg(CSLG)approachtotheFQHEmakesuseofthefactthatin2dimension

8、sanelectroncanbetreatedasabosontowhichanoddnumberofmagnetic uxquantaareattached.Forllingfactors=1=(2k+11)thegroundstateisjustahomogeneousbosoniceld.Thetopologicallytrivial uctuationsaroundtheuniformstatearegapedascanbeeasilyse