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1、REVIEWSOFMODERNPHYSICS,VOLUME82,JANUARY–MARCH2010Colloquium:ArealawsfortheentanglemententropyJ.EisertInstituteofPhysicsandAstronomy,UniversityofPotsdam,14469Potsdam,Germany;BlackettLaboratory,ImperialCollegeLondon,PrinceConsortRoad,LondonSW72BW,UnitedKingdom;andIn
2、stituteforMathematicalSciences,ImperialCollegeLondon,ExhibitionRoad,LondonSW72PG,UnitedKingdomM.CramerandM.B.PlenioBlackettLaboratory,ImperialCollegeLondon,PrinceConsortRoad,LondonSW72BW,UnitedKingdomandInstitutfürTheoretischePhysik,Albert-Einstein-Allee11,Univers
3、itatUlm,D-89069Ulm,GermanyPublished4February2010Physicalinteractionsinquantummany-bodysystemsaretypicallylocal:Individualconstituentsinteractmainlywiththeirfewnearestneighbors.Thislocalityofinteractionsisinheritedbyadecayofcorrelationfunctions,butalsoreßectedbys
4、calinglawsofaquiteprofoundquantity:theentanglemententropyofgroundstates.Thisentropyofthereducedstateofasubregionoftenmerelygrowsliketheboundaryareaofthesubregion,andnotlikeitsvolume,insharpcontrastwithanexpectedextensivebehavior.SuchÒarealawsÓfortheentanglementent
5、ropyandrelatedquantitieshavereceivedconsiderableattentioninrecentyears.TheyemergeinseveralseeminglyunrelatedÞelds,inthecontextofblackholephysics,quantuminformationscience,andquantummany-bodyphysicswheretheyhaveimportantimplicationsonthenumericalsimulationoflattice
6、models.InthisColloquiumthecurrentstatusofarealawsintheseÞeldsisreviewed.Centerstageistakenbyrigorousresultsonlatticemodelsinoneandhigherspatialdimensions.Thedifferencesandsimilaritiesbetweenbosonicandfermionicmodelsarestressed,arealawsarerelatedtothevelocityofinfo
7、rmationpropagationinquantumlatticemodels,anddisorderedsystems,nonequilibriumsituations,andtopologicalentanglemententropiesarediscussed.Thesequestionsareconsideredinclassicalandquantumsystems,intheirgroundandthermalstates,foravarietyofcorrelationmeasures.AsigniÞcan
8、tproportionisdevotedtotheclearandquantitativeconnectionbetweentheentanglementcontentofstatesandthepossibilityoftheirefÞcientnumericalsimulation.Matrix-p
