coherence temperature in the diluted periodic anderson model n. c. costa资料.pdf

该【coherence temperature in the diluted periodic anderson model n. c. costa资料 】是由【dt83088549】上传分享，文档一共【7】页，该文档可以免费在线阅读，需要了解更多关于【coherence temperature in the diluted periodic anderson model n. c. costa资料 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。PHYSICALREVIEWB99,195116(2019),-Santos,,,,ísica,UniversidadeFederaldoRiodeJaneiro,,21941-972RiodeJaneiroRJ,Brazil2TheAbdusSalamInternationalCentreforTheoreticalPhysics,stradaCostiera11,34151Trieste,Italy3DepartmentofPhysics,UniversityofCalifornia,Davis,California95616,USA(Received21December2018;revisedmanuscriptreceived17April2019;published9May2019)TheKondoandperiodicAndersonmodel(PAM)areknowntoprovideamicroscopicpictureofmanyofthefundamentalpropertiesofheavy-fermionmaterialsand,moregenerally,,weapplythedeterminantquantumMonteCarlomethodtoincludedisorderinthePAM,speci??,eentwinedinaheavy-fermion?uid,?ofdopedheavyfermions,andwealsoshowthat,withinthistheoreticalframework,,:.[19–23],[1,2]tophysicssinceitactstolimitthegrowthofcharge-orderedheavyfermions[3–5]andironpnictides[6,7]aremovedwithregions[24].Likewise,dopantdisordercanstabilizelocalizedpressure,chemicaldoping,ic(AF)regions,explainingthepersistenceicorderisdominant,anincrediblevarietyofofAFevendeepinthed-wavephase[25].Asimilarphe-alternatepatternsofspin,charge,-fermionmaterialswhereAFlong-petitionhasbeenanongoingrangeorderisinducedviaCddopingofCeCoIn5[22,26].Ofchallengetothecondensed-munity[8].particularinterestisthecrossoverbetweenKondoscreeningToaddressthesephenomena,icresonanceinthesingle-impuritylimitandcollectivescreeningwith(NMR)hasbeenextensivelyusedtoexplorelocalmicro-,providinggreatin-Apowerfulapproachtoinvestigatethesecrossoverregimessightintotheirnature[9–11].Inparticular,NMRexperimentsistosystematicallyreplacethef-ichavedeterminedtheenergyscaleatwhichaheavy--stateemerges,.,,withsomespatialregionsfavoringstrongspincorre-Thisscalehasbeenassociated[12–18]withacoherence?lations,,T,whosesignatureappears,.,asananomalyThus,insteadofhavingasingleexternalparameterthatglob-inKnightshift(KS)measurements:ic/icbound-icsusceptibility,formostheavy-ary,oneshouldalsoinvestigatehowthephysicalquantitiesfermionmaterialsthistrackingbreaksdownbelowacer-?behaveinthepresenceofinternalandhighlyinhomogeneoustaintemperature,whichisidenti?edwithT[12,13].?andicthespin-latticerelaxationratetohaveastrongdependencesusceptibilityinthesematerials,inparticulartheonefromawithimpuritydoping(.,LasubstitutiononCe--singletd-fchannelthatdelocalizes4f-electrons,leadstothispounds)andevenacquireadistributionofvaluesdependinganomaly,signalingtheemergenceofaheavy-[27–33].Indeed,NMRRemarkably,whentheKSanomalyissingledoutbyremov-andscanningtunnelingmicroscopy(STM)measurementsoningthehigh-temperaturecontributiontothesusceptibility,thecuprateshaveexaminedthelinksbetweenchargeorder,manyheavy-fermionmaterialsexhibitauniversalbehaviorsuperconductivity,andpseudogapphysicsinthecuprates.?fortemperaturesbelowT[12,13].Thecoherencetemper-Fromatheoreticalpointofview,thenatureoftheseatureisevidentinmultipleexperimentalprobes,includingemergentphenomenamaybedescribedbysimpli?edmodelstransport,thermodynamic,andtunnelingmeasurements,ounttheirmostfundamentalmechanisms,itsmicroscopicorigin,anditsrelationtotheKondoscreeningsuchastheperiodicAndersonmodel(PAM)[34–38]andthetemperature,remainopenquestions[17–19].closelyrelatedKondolatticemodel[39–43],whichconsider2469-9950/2019/99(19)/195116(7)195116-1?,195116(2019)weaklycorrelated“conduction”electronshybridizedwithonthef-orbitalandthepossibilityofc-fmixing(duetothestronglycorrelated“localized”).thehybridizationinthesemodelsleadstoaquantumphaseTheDQMCmethod[54–59]employedheretosolvetransition(QPT),inwhichthegroundstateevolvesfromanEq.(1)monlyusedtoinves-ic(AF)-likeHamiltonians:itmapsad-dimensionalnumericalworkonthehomogeneousPAMhascapturedthequantumsysteminaclassical(d+1)-dimensionalone,viaKSanomalyandprovidedT?byquantitativelycharacterizingtheinclusionofanimaginary-,oneseparatestheone-body(K?)andtwo-body(P?)[44,45].Inthecontextofimpuritydoping[46],thePAMpiecesinthepartitionfunctionbyusingtheTrotter-Suzukiposition,.,byde?ningβ=Lττ,withLτbeingthearounddopedimpuritiesinCeCo(In1?xCdx)5[47–49],andnumberofimaginary-timeslices,and[50,51],asintheZ=?βH?=?τ(K?+P?)LτcaseofCeCo(In1?xSnx)5[23,52].TreTr[(e)]binationofrandomnessandstrong≈e?τK?e?τP?e?τK?e?τP?···,interactionswithanexactnumericalapproach,whichallowsTr[](2)for“real-spaceimaging”(τ)-limitτ→-fermionmaterials,suchasinquadratic(single-body)formthroughadiscreteHubbard-inCe1?xLaxCoIn5,uratelyStratonovichtransformation(HST)onthetwo-bodyterms,?τP??eldswithisonwhetherthecalculatedtrendsofthesequantitiesre-componentsoneachofthespaceandimaginary-timelatticesemblethosefromexperimentalNMRmeasurements[31]oncoordinates,,wechoosetτ=,sothattheerrorfromTothisend,weextendprevious[44]determinantquantumtheTrotter-positionislessthan,parableMonteCarlo(DQMC)simulationstotreattherandomlyto,(dPAM),-andtwo-?ndings,fromwhichourkeyfunctions,suchassusceptibilities,-resultsareasfollows:(i)?,eveninthepresenceofdisorder;Althoughnumericallyexact,DQMCisconstrainedby(ii)T?increaseswithhybridizationV(orpressure);andtheinfamousminus-signproblem[57,59],whichrestricts(iii)-ouranalysestothehalf-?llingcase,.,whenbothc-andnally,(iv)theNMRrelaxationrate,1/T,exhibitsastrongly,1f-orbitalshavencf=1/-i,σstratethatseveralofthemostfundamentalconclusionsofCarloisespeciallywell-matchedtoanalyzetheproblemofNMRexperimentscanbepredicted,includingthescalingbe-disorderandthelocalstructuresthatformaroundanimpurity,haviorofT?.,manytypesofrandomness,suchaslocalvariationsinhybridization,on-siterepulsion,andsiteremoval,donotaffectparticle-,thereisnosignproblemathalf-?lling,TheHamiltonianforthedPAMreads[53]regardlessofthepresenceofdisorder(dilution)onthelattice.ThisallowsustoinvestigatethebehaviorofcorrelationsinallH=??+..??+..t(ciσcjσHc)Vi(ciσfiσHc)temperaturescales.i,j,σi,σToconnectwithNMRmeasurements,thecentralquanti-icsusceptibilities,fromwhichtheαff1f1?μnσ+Un?n?,(1)Knightshiftandspin-latticerelaxationrateareobtained;seeiii↑2i↓2i,σ,,thetotalspinona=c+f≡wherethesumsrunoveratwo-dimensionalsquarelattice,givensiteiisSiSiiSi,withi1atsitescontainingwithi,jdenotingnearest-neighborsites,andα=corf;f-orbitals,,icsuscepti-?rsttermbilityisgivenbycorrespondstothehoppingofconductionelectrons(thehop-χ=χcc+2χcf+χff,(3)pingintegral,t,setstheenergyscale),whilethelasttermdescribestheCoulombrepulsiononlocalizedf-hybridizationbetweenthesetwoorbitalsismodeledbyaβ1ααααsite-dependenthoppingViχαα=QdτS(τ)·S(0).(4)NijijHereweconsiderfullorbitaldilution,inwhichweran-sij0domlysetUi=Vi=,ατ=τHα?τHα,α=pletelyremovingf-orbitals,similarlyHereSi()eSi(0)e,withcorf,andαα10=δ+δδ+δδ+δδic4fCeatombya4fLaQij[(α,cijα,f)α,α(iα,fα,cjα,cα,f)];oneinCeCoIn5,whichlocallysuppressesboththemomentthenumberoflatticesitesisNs=L×,theKnight195116-2COHERENCETEMPERATUREINTHEDILUTEDPERIODIC…PHYSICALREVIEWB99,195116(2019)±±±±±±χχχχ×.(a)Knightshiftasafunctionoftotalsusceptibilityχ.(b)χandtherenormalizedKnightshiftK?asafunctionoftemperature,for?V/t==?nesT/t=(seetext).(c)ExperimentalNMRresultsforCe1?xLaxCoIn5reproduced?fromRef.[31].(d)DatacollapseofDQMCresultsfortheKSanomaly,KHF,forT,andinallsubsequent?gures,whennotshown,(hencethepresenceofdelocalized4felectrons),providesanimportanttooltoinvestigatetheemergenceofaheavy-K=Aχ+A+Bχ+Bχ+K,cc()cfff0(5)(B)correspondstothehyper?necouplingbetweenpersistseveninstronglydilutedmaterials,asdisplayedinthenuclearspinofIn(1)atomsandconduction(localized)(c),fortheheavy-fermionCe1?xLaxCoIn5,withx≈.-,,whichthecoherencetemperatureinthepresenceofdisorderatadependsonthedistributionofnearest-neighborsite(Ceorvaluesimilartothatofthepuresystem[44,61]isanontrivialLa)momentstothecentralIn(1)atom[31].Thus,,electronsinunpairedorbitals(whichcorrespondtotheaverageKofrepresentativesitesthatcouplesurvivedilution)?necouplingsaresusceptibility,regardlessofwhethertheyareconductingorgenerallydifferent[12,60],andstronglymaterial-dependent,localized[49,62,63].Thiscould,inprinciple,signi?cantlywefollowapreviousstudy[44]andtakeA/B=;generalaffecttheassumptionsunderwhichK?wouldtrackχ,hence?trendsarenotsensitivetotheprecisechoiceofA/B[44].,theseeffectsaresimulationscapturequalitativefeaturesofχ,K,and1/T1,butmorerelevantatverylowtemperatures,duetothepossibilitynotmaterial-speci?,ourDQMCdataoflong-–30differentdisordercon?gurationsonweakdependenceoftheNMRquantitieswithdilution,asa10×10squarelattice,andUf/t=(a)–1(c),isanimportantsteptowarda?wereobtainedforV1,[37,38].Withinatwo-?uidmodel[12,13,28,64,65],onesinglesoutthe“heavy-fermion?uid”contributiontotheKSbysubtract-“normal”(high-temperature)contribution,.,≡?,localizedelectronsareweaklycou-KHFBeff(K)(7)pledtoconductionbands,sothecontributionofχandχcccfRemarkably,,theKnightshift[Eq.(5)]ofKformanydifferentheavy-fermionmaterials,tracksthelocalizedelectronsusceptibilityand,underthesameHFassumptions,(T)HF=f(T)≡(1?T/T?)3/2[1+ln(T?/T)],(8)theprocedureadoptedina