Contents - Max-Planck-Institut für Physik komplexer Systeme
Contents - Max-Planck-Institut für Physik komplexer Systeme
Contents - Max-Planck-Institut für Physik komplexer Systeme
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ResearchGroup:NewStatesofQuantumMatter<br />
(Head:Dr.A.Läuchli)<br />
Theresearchgroup”Newstatesofquantummatter”starteditsactivityatthe mpipksinSeptember<br />
2008. Itpresentlyhoststhreepostdoctoralmembers(V.Alba,D.CharrierandI.Rousochatzakis)as<br />
wellasthreeassociatedmemberswithinthecondensedmatterdepartment(E.Bergholtz,M.Haque<br />
andD.Kovrizhin). Wealsoenjoyedthepresenceofseveralvisitorsforshortertermresearchactivities<br />
(K.Agarwal,B.Chakrabarti,B.Hetenyi,D.SchwandtandS.Wenzel).<br />
Thegoalofourresearchgroupistounderstandstronglycorrelatedquantumsystemsbasedonnumerical<br />
simulationsandtouncoverandcharacterizenewquantumstatesemerginginthesesystems.Westudy<br />
problemsrangingfromquantummagnetismandultracoldatomicgasestosuperconductivityandthe<br />
fractionalquantumhalleffect.Duringthereportperiodweworkedparticularlyonthefollowingtopics:<br />
EntanglementPropertiesoftheFractionalQuantumHallstates—Weputforwardanewapproach<br />
toobtainingthescalingbehavioroftheentanglemententropyinfractionalquantumHallstatesfrom<br />
finite-sizewavefunctions.Byemployingthetorusgeometryandthefactthatthetorusaspectratiocan<br />
bereadilyvaried,wecanextracttheentanglemententropyofaspatialblockasacontinuousfunction<br />
oftheblockboundary. Otherthanthetopologicalinformation,thestudyofentanglementscalingis<br />
alsousefulasanindicatorofthedifficultyposedbyfractionalquantumHallstatesforvariousnumerical<br />
techniques. WealsoanalyzedtheentanglementspectrumofLaughlinstatesonthetorusandshowed<br />
thatitisarrangedintowers,eachofwhichisgeneratedbymodesoftwospatiallyseparatedchiraledges.<br />
Thisstructureispresentforalltoruscircumferences,whichallowsforamicroscopicidentificationof<br />
theprominentfeaturesofthespectrumbyperturbingaroundthethintoruslimit.Wearecurrentlyalso<br />
investigatingthestructureofentanglementspectraforotherquantummanybodysystems.<br />
NovelorderedphasesandspinliquidsinthevicinityofMotttransitions—WhiletheMotttransition<br />
andthephasesinitsvicinityarequitewellunderstoodforHubbardmodelsoftwo-flavoredfermions(e.g.<br />
electrons)onhypercubiclattices,thesamedoesnotholdtruewheneitherincreasingthenumberof<br />
flavorstothreeormore-ascouldbepossibleforearth-alkalineatomsinanopticallattice-orwhen<br />
consideringmorecomplexlatticessuchasthetriangularorthehoneycomblattice. Wemadeprogress<br />
alongtheselinesusingcomputationaltechniquestorevealthenatureoftheMottinsulatingstateof<br />
threeflavoredfermionsonseveralrealisticlattices,andprovideevidenceforaspinliquidphasecloseto<br />
theMotttransitionoftwo-flavoredfermionsonthetriangularlatticewhichisofpossiblerelevancefora<br />
classoforganicconductors.<br />
Criticalpropertiesoforbital-onlymodels—Orbital-onlymodelsemergedrecentlyasprototypesystems<br />
enablingtheunderstandingofrelevantaspectsofthecollectivedynamicsoforbitaldegreesoffreedom.<br />
Inadifferentcontext,orbital-likemodelsareattractingconsiderabletheoreticalinterestduetotheir<br />
abilitytosustaintopologicallyorderedphaseswithpossiblyanyonicexcitations,asexemplifiedbythe<br />
Kitaevhoneycombmodel. Avarietyofpropertieshavealreadybeenuncoveredfororbital-onlymodels,<br />
butmostofthesearerestrictedtogroundstateorlow-temperatureproperties. Muchlessisknown<br />
aboutfinite-temperaturepropertiesandinparticularthenatureofthermalphasetransitions. Wehave<br />
nowperformedacomprehensiveMonteCarloinvestigationofthenatureofthefinite-temperaturephase<br />
transitionsintwopopularorbital-onlymodelsonthethree-dimensionalcubiclattice:the egandthe t2g<br />
models. The egmodeldisplaysacontinuousphasetransitiontoanorbitallyorderedphase. Adetailed<br />
analysisofthecriticalexponentsrevealssignificantdeviationsfromthewellknownsetofexponentsof<br />
the O(N)familiy. Furthermoreat Tca U(1)symmetryemerges,whichpersistsfor T < Tcbelowa<br />
crossoverlengthscalingas Λ ∼ ξ a ,withanunusuallysmall a ≈ 1.3.Forthe t2gmodelwefindhowever<br />
afirstordertransitionintoalow-temperaturelattice-nematicphasewithoutorbitalorder.<br />
Algorithmicdevelopments—Wemadealgorithmicprogressontwosides. Ontheonehand,weput<br />
forwardanewformulationofthehybridizationexpansioncontinuous-timeQuantumMonteCarloalgorithmforsingleimpurityproblems(relevante.g.fordynamicalmean-fieldtheory(DMFT)applications),<br />
whichsystematicallyexploitsthesparsestructureoftheimpurityhamiltonianstoachieveasignificant<br />
speedupcomparedtothepreviouslyuseddensematriximplementation.Usingthisnewformulationitis<br />
nowpossibletoperformDMFTsimulationsbasedonfullySU(2)invariantinteractionssuchasHund’s<br />
termsfor3dtransitionmetalcompounds.Asecondlineofalgorithmicdevelopmentistoparallelizeour<br />
existingexactdiagonalizationcodesforquantumspinsystemsformassivelyparalleldistributedmemory<br />
20 ScientificWorkanditsOrganizationatthe<strong>Institut</strong>e–anOverview
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