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1、DENSITY-FUNCTIONALTHEORYFORTHEHUBBARDMODEL:NUMERICALRESULTSFORTHELUTTINGERLIQUIDANDTHEMOTTINSULATORK.CapelleDepartamentodeQu´ımicaeF´ısicaMolecularInstitutodeQu´ımicadeSao˜Carlos,UniversidadedeSao˜Paulo,CaixaPostal780,Sao˜Carlos,13560-970SP,BrazilN.A.Lima,M.F.Silva,andL.N.Olive
2、iraDepartamentodeF´ısicaeInformatica´InstitutodeF´ısicadeSao˜Carlos,UniversidadedeSao˜Paulo,CaixaPostal369,13560-970Sao˜Carlos,SP,BrazilAbstractWeconstructandapplyanexchange-correlationfunctionalfortheone-dimensio-nalHubbardmodel.ThisfunctionalhasbuiltintoittheLuttinger-liquida
3、ndMott-insulatorcorrelations,presentintheHubbardmodel,inthesamewayinwhichtheusualabinitiolocal-densityapproximation(LDA)hasbuiltintoittheFermi-liquidcorrelationspresentintheelectrongas.Anaccurateexpressionfortheexchange-correlationenergyofthehomogeneousHubbardmodel,basedontheBe
4、theAnsatz(BA),isgivenandtheresultingLDAfunctionalisappliedtoavarietyofinhomogeneousHubbardmodels.Theseincludefinite-sizeHubbardchainsandrings,varioustypesofimpuritiesintheHubbardmodel,spin-densitywaves,andMottinsulators.Forsmallsystems,forwhichnumericallyexactdiag-onalizationisf
5、easible,wecomparetheresultsobtainedfromourBA-LDAwiththeexactones,findingverysatisfactoryagreement.Intheoppositelimit,largeandcomplexsystems,theBA-LDAallowstoinvestigatesystemsandparameterregimesthatareinaccessiblebytraditionalmethods.1.TheHubbardmodelanddensity-functionaltheoryT
6、heHubbardmodelisoneofthemostvenerablemodelsofmany-bodyphysics.Originallyitwasproposedasasimplifieddescriptionofmagnetismintransitionmetals[1,2].Thisrequiredthemodeltobeformulatedonathree-dimensionallattice.Interestinthetwo-dimensionalHubbardmodelismorerecent,andlargelyduetoAnder
7、son'ssuggestionthatitcontainsthecorrect12minimalrequirementsneededfordescribingthecupper-oxideplanesincupratehigh-temperaturesuperconductors[3].InonedimensiontheHubbardmodelhasattractedinterestmainlybecauseitpresentsafascinatingphasediagram,includingLuttingerliquidandMottinsula
8、tingphaseswhichareatthecenterofmuchrecentworkonstrongl
