Weak first-order superfluid--solid quantum phase transitions

We study superfluid--solid zero-temperature transitions in two-dimensional lattice boson/spin models by Worm-Algorithm Monte Carlo simulations. We observe that such transitions are typically first-order with the exception of special high-symmetry points wh

WeakFirst-OrderSuper uid–SolidQuantumPhaseTransitions

1

AnatolyKuklov1,NikolayProkof’ev

2,3

,andBorisSvistunov

2,3

arXiv:cond-mat/0406061v1 [cond-mat.stat-mech] 2 Jun 2004

DepartmentofEngineeringScienceandPhysics,TheCollegeofStatenIsland,

CityUniversityofNewYork,StatenIsland,NewYork10314

2

DepartmentofPhysics,UniversityofMassachusetts,Amherst,MA010033

RussianResearchCenter“KurchatovInstitute”,123182Moscow

Westudysuper uid–solidzero-temperaturetransitionsintwo-dimensionallatticeboson/spinmodelsbyWorm-AlgorithmMonteCarlosimulations.Weobservethatsuchtransitionsaretyp-ically rst-orderwiththeexceptionofspecialhigh-symmetrypointswhichrequire netuningintheHamiltonianparameterspace.Wepresentevidencethatthesuper uid–checkerboardsolidandsuper uid–valence-bondsolidtransitionsathalf-integer llingfactorareextremelyweak rst-ordertransitionsandinsmallsystemstheymaybeconfusedwithcontinuousorhigh-symmetrypoints.

Recently,therehasbeenanincreasedinterestinsuper uid–solid(SF-S)quantumphasetransitionsinlat-ticeboson/spinsystems[1,2,3,4].[By‘solid’wemeananinsulatingstatefeaturingthebrokentransla-tionsymmetry—likecheckerboardsolid/antiferromagnet(CB)orvalencebondsolid(VBS),asopposedtotheMottinsulatorwhichpreservesthetranslationsymme-try.]Ononehand,thisinterestisstimulatedbyexperi-mentalperspectivesofstudyingsuchtransitionsinopti-callatticesontheotherhand,theSF–VBStransitionina(2+1)-dimensionalsystemhasbeenarguedtobethesimplestexampleofqualitativelynewtypeofquan-tumcriticality,thatdoesnot tthestandardLandau-Ginzburg-Wilsonparadigm[4].IntriguingdataontheSF-StransitionswereobtainedbydirectMonteCarlosimulationsofquantumsystems[1,2].Itwasobserved[1]thattheSF-CBtransitioninthehard-corebosonicmodelwithnearest-andnext-nearest-neighborinteractionre-mainsremarkablyinsensitivetotheexplicitHeisenbergsymmetrybreaking.Thetransitionisnumericallyindis-tinguishablefromthatoftheHeisenbergspin-1/2model:adegenerate(hysteresisless)transition.Insimulationsofthe2DquantumXYmodelwithringexchangetheSF-VBStransitionwasinterpretedasthesecond-orderone,whichsuggesteditsunderstandingintermsofthedecon nedquantumcriticalpoint[4].

InthisLetter,weperformacareful nite-sizeanaly-sisoftheSF-CBandSF-VBStransitionsbysimulatingageneralized(2+1)-dimensionalJ-currentmodel[5],whichisadiscrete-imaginary-timeanalogofthequantumbo-son/spinlatticesystem.Thesimplicityand exibilityofourmodelincombinationwiththee cientWormAlgo-rithmallowustoarriveatade nitiveconclusionthatinSF-CBandSF-VBScaseswearedealingwithanoma-louslyweak rst-orderphasetransitions.Moreover,thetwotransitionsareremarkablysimilartoeachother.Inbothcases,smallenoughcriticalsystemsmimicthebe-haviorofahighlysymmetricmodelwithbrokensymme-try.TheSF-CBcasecorrespondstotheO(3)-symmetryoftheHeisenbergmodel,whileintheSF-VBScaseweclearlyseeaquasi-O(4)behaviorthatmanifestsitselfasacoexistenceatthecriticalpointofthesuper uidre-sponseandboth(x-andy-)VBSorders,inarbitrary

proportions.

Wecon neourselvestothecasewhenthestatisticsof(2+1)-dimensionalparticletrajectoriesinimaginarytime(worldlinecon gurations)ispositivede nite.Whatgroundstatescanemergeunderthiscondition?Thestatewithchaotic(unstructured)typicalworldlinecon gura-tionisSF.Indeed,theabsenceofstructureimplies uc-tuationsoftheworldlinewindingnumbers,W,andthusa nitesuper uidresponsewhichisgivenbythemeansquareofWseeEq.(4)below.[Onecanhardlyextendthisargumenttocaseswhenthecon gurationweightisnotpositivede nite,sincethenotionofatyp-icalcon gurationbecomesvague.]InSF,theU(1)sym-metryisbroken(atleastinatopologicalsense).Theonlywaytorestorethissymmetryistosuppress uctuationsofWwhichseemstobeimpossiblewithoutstructur-ingworldlinecon gurationsinsuchawaythatforeachimaginary-timemomentthepositionofeachworldlineinthecorrespondingreal-spaceplanecanbeunambigu-ouslyassociatedatthemicroscopiclevelwithoneofthelatticesites/bonds,andviceversa.Ifthetotalnum-beroftheworldlinesisnotequaltoamultipleofthenumberofsites/bonds,thestructuredworldlinecon gu-rationimmediatelyimpliesabrokentranslationsymme-try.Thisconsiderationleadstotheconjecturethatformodelswiththepositivede nitestatisticsofworldlinecon gurationsandnon-integer llingfactorthegenericgroundstateshouldfeatureanorder,eitherSForsolid,orboth(supersolid).Groundstateswithnonesymmetrybeingbroken(“quantumdisorder”)maythenoccuronlyascriticalpointsseparatingtheorderedstates.

Inthepath-integralrepresentation,weseenoquali-tativedi erencebetweenthesite-andbond-basedsolidssincebotharecharacterizedbytheworldlinestructuring,intheabove-mentionedsense.Ineithercase,zero-point uctuationsnecessarilyincludepermutationsoftwoandmorelines,andthusonlargescalessuchmicroscopicde-tailsasthemostprobablepositioning—onsitesoronbonds—oftheworldlinescanhardlyberelevanttotheuniversalpropertiesoftheSF–Stransition.Theonlypropertythatseemtobecrucialisthesymmetryoftheemerginglattice.

Intermsofalgorithmicsimplicityandnumericalef-

We study superfluid--solid zero-temperature transitions in two-dimensional lattice boson/spin models by Worm-Algorithm Monte Carlo simulations. We observe that such transitions are typically first-order with the exception of special high-symmetry points wh

tems.Acloserlookatthetransitionpointisprovidedintheinsets.Errorbarsareshownforallpoints(insomecasesthesearesmallerthanthesymbolsize).

ciency,classical(d+1)-dimensionalanalogsofd-dimensionalquantumsystemso erasigni cantadvan-tage.Thisapproachwassuccessfullyusedpreviouslyinthestudiesofdisordered[5,7,8]andtwo-componentsystems[9].Inaddition,classicalmodelso ermorefree-domin“designing”e ectivemodelswithcomplexphasediagrams.Theso-calledJ-currentmodelofRef.[5]isobtain …… 此处隐藏：14046字，全部文档内容请下载后查看。喜欢就下载吧 ……