Renormalization Group Analysis of Multi-Band Many-Electron Systems at Half-Filling

Journal of Mathematical Sciences

Kashima, Yohei¹ 

关键词: Many-electron system;    renormalization group;    the Hubbard model;    zero-temperature limit.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Renormalizationgroupanalysisformulti-bandmany-electronsystemsathalf-fillingatpositivetemperatureispresented.TheanalysisincludestheMatsubaraultra-violetintegrationandtheinfraredintegrationaroundthezerosetofthedispersionrelation.Themulti-scaleintegrationschemesareimplementedinafinite-dimensionalGrassmannalgebraindexedbydiscreteposition-timevariables.Inorderthatthemulti-scaleintegrationsarejustifiedinductively,variousscale-dependentestimatesonGrassmannpolynomialsareestablished.Weapplythesetheoriesinpracticetoprovethatforthehalf-filledHubbardmodelwithnearest-neighborhoppingonasquarelatticetheinfinite-volume,zero-temperaturelimitofthefreeenergydensityexistsasananalyticfunctionofthecouplingconstantinaneighborhoodoftheoriginifthesystemcontainsthemagneticflux$pi$(mod$2pi$)perplaquetteand$0$(mod$2pi$)throughthelargecirclesaroundtheperiodiclattice.CombinedwithLieb'sresultonthefluxphaseproblem([Lieb,E.H.,Phys.Rev.Lett.$f73$(1994),2158]),thistheoremimpliesthattheminimumfreeenergydensityofthefluxphaseproblemconvergestoananalyticfunctionofthecouplingconstantintheinfinite-volume,zero-temperaturelimit.Theproofofthetheoremisbasedonafour-bandformulationofthemodelHamiltonianandanextensionofGiuliani-Mastropietro'srenormalizationdesignedforthehalf-filledHubbardmodelonthehoneycomblattice([Giuliani,A.andV.Mastropietro,Commun.Math.Phys.$f293$(2010),301--346]).

【 授权许可】

Unknown