Topological Orders and Edge Excitations in Fractional Quantum Hall States

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1、TopologicalOrdersandEdgeExcitationsinFractionalQuantumHallStatesXiao-GangWenDepartmentofPhysics,MIT,77MassachusettsAvenue,Cambridge,MA02139,USAFractionalquantumHall(FQH)liquidscontainextremelyrichinternalstructureswhichrepresentacompletelynewkindofordering.Wediscussthecharacterizationandcla

2、s-sificationoftheneworders,generallycalledtopologicalorders.WealsodiscussedgeexcitationsinFQHhquidswhichprovideuswithapracticalwaytomeasuretopologicalorderinexperiments.1IntroductionThefractionalquantumHall(FQH)effectappearsintwo-dimensionalelectronsystemsinastrongmagneticfield.Sinceitsdisc

3、overyin1982[1],experimentsonFQHsystemscontinuedtorevealmanynewphenomenaandsurprises,indicatingthattheelectronsystemswithfractionalquantumHalleffect(whicharecalledFQHliquids)containextremelyrichinternalstructures.Infact,FQI-Iliquidsrepresentacompletelynewstateofmatter.Oneneedstodevelopnewcon

4、ceptsandnewtechniquestounderstandthesenewkindofstates.Gasesrepresentsomeofthesimplestsystems.Themotionofamoleculeinagashardlydependsonthepositionsandmotionofothermolecules.Thusgasesareweaklycorrelatedsystems.Themotionsofmoleculesinagasareveryclosetothemotionsoffreeparticles.Thisallowsustoca

5、lculateeasilythephysicalpropertiesofagasstartingfromafreeparticlesystem.Aswelowerthetemperature,themotionofmoleculesinagasbecomemoreandmorecorrelatedwithothermolecules.Belowacertaintemperaturethemotionofmoleculesiscompletelycorrelatedandthemoleculesformacrystalwhichisastronglycorrelatedsyst

6、em.Inacrystalanindividualatomcanhardlymovebyitself.Excitationsinacrystalalwayscorrespondtocollectivemotionofmanyatoms(whicharecalledphonons).FQHliquidsrepresentanotherkindofstronglycorrelatedstructure.Sinceelectronsaremuchlighterthanatoms,theirmotionismuchstrongerdeterminedbyquantumconsider

7、ations.ThesequantumfluctuationspreventelectronsinaFQHsystemtoformacrystal.Nevertheless,themotionoftheelectronsinFQHliquidsarehighlycorrelated.AlltheelectronsinaFQHliquid"dancecollec-tively",followingastrictlyglobaldancingpatternwhichminimizesthegroundsta