Singular or non-Fermi liquids

C.M.Varmaetal./PhysicsReports361(2002)267–417271

ThesolutionoftheKondoproblemandtherealizationthatitslow-temperaturepropertiesmaybediscussedinthelanguageofFLThasledinturntotheformulationandsolutionofimpuritymodelswithsingularlow-energyproperties.SuchmodelshaveaQCPforaparticu-larrelationbetweenthecouplingconstants;insomeexamplestheyexhibitaquantumcriticalline.ThethermodynamicandtransportpropertiesaroundsuchcriticalpointsorlinesarethoseoflocalsingularFermiliquids.Althoughthedirectexperimentalrelevanceofsuchmodels(asofone-dimensionalmodels)toexperimentsisoftenquestionable,thesemodels,beingsol-uble,canbequiteinstructiveinhelpingtounderstandtheconditionsnecessaryforthebreak-downofFLTandassociatedquasiparticleconcepts.Theknowledgefromzero-dimensionalandone-dimensionalproblemsmustneverthelessbeextrapolatedwithcare.

AproblemwhichwedonotdiscussbutwhichbelongsinthestudyofSFLsisthequantumHalle ectproblem.Themassivedegeneracyoftwo-dimensionalelectronsinamagneticÿeldleadstospectacularnewpropertiesandinvolvesnewfractionalquantumnumbers.TheessentialsofthisproblemweresolvedfollowingLaughlin’sinspiredvariationalcalculation.Theprincipalreasonfortheomissionisÿrstlythatexcellentpapersreviewingthedevelopmentsareavailable[213,72,111]andsecondlythatthemethodologyusedinthisproblemisingeneraldistinctfromthosefordiscussingtheotherSFLswhichhaveacertainunity.WewillhoweverhaveoccasionstorefertoaspectsofthequantumHalle ectproblemoften.EspeciallyinterestingfromourpointofviewistheweaklysingularFermiliquidbehaviorpredictedinthe =quantumHalle ect[118].

Withlessjustiÿcation,wedonotdiscusstheproblemofsuperconductortoinsulatorand=ortometaltransitionsintwo-dimensionaldisorderedsystemsinthelimitofzerotemperaturewithandwithoutanappliedmagneticÿeld.Interestingnewdevelopmentsinthisproblemwithreferencestosubstantialearlierworkmaybefoundin[176,177,247].TheproblemoftransitionsinJosephsonarrays[247]isavariantofsuchproblems.

OneoftheprincipalaspectsthatwewanttobringtotheforegroundinthisreviewisthefactthatSFLsallhaveincommonsomefundamentalfeatureswhichcanbestatedusefullyinseveraldi erentways.(i)TheyhavedegenerategroundstatestowithinanenergyoforderkBT.Thisdegeneracyisnotduetostaticexternalpotentialsorconstraintsasin,forexamplethespin-glassproblem,butdegeneracieswhicharedynamicallygenerated.(ii)Suchdegeneraciesinevitablyleadtoabreakdownofperturbativecalculationsbecausetheygenerateinfra-redsingularitiesinthecorrelationfunctions.(iii)Ifabareparticleorholeisaddedtothesystem,itisattendedbyadivergentnumberoflow-energyparticle–holepairs,sothattheone-to-onecorrespondencebetweentheone-particleexcitationoftheinteractingproblemandthoseofthenon-interactingproblem,whichisthebasisforFLT,breaksdown.(iv)SinceSFLsareconcernedwithdynamicallygenerateddegeneracieswithinenergiesoforderofthemeasuringtemperature,theobservedpropertiesaredeterminedbyquantum-mechanicaltoclassicalcrossoversandinparticularbydissipationinsuchacrossover.

Onthetheoreticalside,onemaynowviewFermi-liquidtheoryasaforerunneroftherenor-malizationgroupideas.Therenormalizationgrouphasledtoasophisticatedunderstandingofsingularitiesinthecollectivebehaviorofmany-particlesystems.ItislikelythatthesemethodshaveanimportantroletoplayinunderstandingthebreakdownofFLT.

TheaimofthispaperistoprovideapedagogicalintroductiontoSFLs,focusedontheessentialconceptualideasandonissueswhicharesettledandwhichcanbeexpectedto