Fermi liquid features of the one-dimensional Luttinger liquid

Fermi liquid features of the one-dimensional Luttinger liquid

Fermi-liquidfeaturesoftheone-dimensionalLuttingerliquid

1

YupengWang1,2

LaboratoryofUltra-LowTemperaturePhysics,ChineseAcademyofSciences,P.O.Box2711,Beijing100080,China

2

Institutf¨urPhysik,Universit¨atAugsburg,86135Augusburg,Germany

arXiv:cond-mat/9712300v2 [cond-mat.str-el] 28 Apr 1999

Weshowthattheone-dimensional(1D)electronsystems

canalsobedescribedbyLandau’sphenomenologicalFermi-liquidtheory.MostoftheknownresultsderivedfromtheLuttinger-liquidtheorycanberetrievedfromthe1DFermi-liquidtheory.ExactcorrespondencebetweentheLandaupa-rametersandHaldaneparametersisestablished.Theexpo-nentsofthedynamicalcorrelationfunctionsandtheimpu-rityproblemarealsodiscussedbasedonthe nitesizecor-rectionsofelementaryexcitationswiththepredictionsoftheconformal eldtheory,whichprovidesabridgebetweenthe1DFermi-liquidandtheLuttingerliquid.71.10.Pm,71.10.Ay,72.15.Nj

Landau’sFermi-liquidtheory(FLT)[1]isafundamen-talparadigmincondensedmatterphysics.However,assuggestedbymanyauthors,thesituationinreduceddi-mensionsmaybedi erent.Especiallyin1D,itisgen-erallybelievedthatthesystemsaremarginal[2–4]andthelowtemperaturepropertiesofthe1Dgaplessquan-tumsystemscanbedescribedbytheLuttinger-liquidtheory(LLT)[5,6].Evenin2D,AndersonshowedthatastronglycorrelatedelectronsystemmayexhibitthemaincharactersofaLuttingerliquid[7].ALuttingerliquidgenerallyhasthefollowingcharacteristics:(i).Itslowen-ergyexcitationscanbecompletelydescribedbythecol-lectivedensitywaves,i.e.,thesoundwaves(chargeden-sity uctuation)andthespindensitywavescharacterizedbytwovelocitiesvρandvσrespectively;(ii).Variousop-eratorsexhibitanomalousdimensionsdeterminedbytwosti nessconstantsKρandKσ,whichleadtothenonuni-versalpower-lawdecayofcorrelationfunctions;(iii).Themomentumdistributionofthephysicalparticlesiscon-tinuousattheFermisurface.

Infact,thelowtemperaturepropertiesofa1Dgap-lesselectronsystemareuniquelydeterminedbyfourcon-stantsvρ,vσ,KρandKσandtheHaldanerelationshold:vNγvJγ=vγ2,

vJγ=Kγvγ,

γ=ρ,σ

,

(1)

wherevNγandvJγ(γ=ρ,σ)arethevelocitiesofexcita-tionsinducedbyadditionalchargesandcurrents,respec-tively[5,6].Someimportantthermodynamicquantitiessuchasthespeci cheatC,thesusceptibilityχandthecompressibilityκaregivenbyC=

π

πvNσ

,κ=

2

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