Singular or non-Fermi liquids

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survivefuturedevelopments.Therefore,wewillnotattempttogiveanexhaustivereviewoftheliteratureonthisproblemorofalltheexperimentalsystemswhichshowhintsofSFLbehavior.Theexperimentalexampleswediscusshavebeenselectedtoillustratebothwhatisessentiallyunderstoodandwhatisnotunderstoodeveninprinciple.Onthetheoreticalside,wewillshyawayfrompresentingindepththesophisticatedmethodsnecessaryforadetailedevaluationofcorrelationfunctionsnearQCP—forthiswerefertothebookbySachdev[225]—orforanexactsolutionoflocalimpuritymodels(see,e.g.[124,227,259]).Likewise,foradiscussionoftheapplicationofquantumcriticalscalingideastoJosephsonarraysorquantumHalle ects,werefertotheniceintroductionbySondhietal.[247].1.2.Outlineofthepaper

Theoutlineofthispaperisasfollows.WestartbysummarizinginSection2someofthekeyfeaturesofLandau’sFLT—indoingso,wewillnotattempttoretracealloftheingredientswhichcanbefoundinmanyoftheclassictextbooks[208,37];insteadourdiscussionwillbefocusedonthoseelementsofthetheoryandtherelationwithitsmicroscopicderivationthatallowustounderstandthepossibleroutesbywhichtheFLTcanbreakdown.ThisisfollowedinSection3bytheFermi-liquidformulationoftheKondoproblemandoftheSFLvariantsoftheKondoproblemandoftwointeractingKondoimpurities.TheintentionhereistoreinforcetheconceptsofFLTinadi erentcontextaswellastoprovideexamplesofSFLbehaviorwhicho erimportantinsightsbecausetheyarebothsimpleandsolvable.Wethendiscusstheproblemofonespatialdimension(d=1),presentingtheprincipalfeaturesofthesolutionsobtained.Wediscusswhyd=1isspecial,andtheproblemsencounteredinextendingthemethodsandthephysicstod¿1.WethenmovefromthecomfortsofsolvablemodelstotherealityofthediscussionofpossiblemechanismsforSFLbehaviorinhigherdimensions.FirstweanalyzeinSection5theparadigmaticcaseoflong-rangeinteractions.Coulombinteractionswillnotdointhisregard,sincetheyarealwaysscreenedinametal,buttransverseelectromagneticÿeldsdogiverisetolong-rangeinteractions.ThefactthatasaresultnometalisaFermiliquidforsu cientlylowtemperatureswasalreadyrealizedlongago[127]—fromapracticalpointofview,thismechanismisnotveryrelevant,sincethetemperatureswherethesee ectsbecomeimportantareoforder10 16K;nevertheless,conceptuallythisisimportantsinceitisasimpleexampleofagaugetheorygivingrisetoSFLbehavior.Gaugetheoriesonlatticeshavebeenintroducedtodiscussproblemsoffermionsmovingwiththeconstraintofonlyzeroorsingleoccupationpersite.WethendiscussinSection6thepropertiesnearaquantumcriticalpoint,takingÿrstanexampleinwhichtheferromagnetictransitiontemperaturegoestozeroasafunctionofsomeexternallychosensuitableparameter.Wereferinthissectiontoseveralexperimentsinheavyfermioncompoundswhichareonlypartiallyunderstoodornotunderstoodeveninprinciple.WethenturntoadiscussionofthemarginalFermiliquidphenomenologyfortheSFLstateofcopper-oxidehigh-Tcmaterialsanddiscusstherequirementsonamicroscopictheorythatthephenemenologyimposes.Asketchofamicroscopicderivationofthephenemenologyisalsogiven.WeclosethepaperinSection8withadiscussionofthemetallicstateind=2andthestateofthetheorytreatingthedi usivesingularitiesind=2anditsrelationtothemetal–insulatortransition.