One-andtwo-dimensionalAndersonmodelwithlong-rangecorrelated-disorder一維和二維關(guān)聯(lián)無序安德森模型

One-andtwo-dimensionalAndersonmodelwithlong-rangecorrelated-disorderAndersonmodel-IntroductionEntanglementin1D2DEntanglement2Dconductance2Dtransmission2DmagnetoconductanceAndersonmodel-IntroductionWhatisadisorderedsystem?Nolong-rangetranslationalorderTypesofdisorder

(a)crystal(b)Componentdisorder(c)positiondisorder(d)topologicaldisorder

diagonaldisorder

off-diagonaldisordercompletedisorderLocalizationprediction：anelectron,whenplacedinastrongdisorderedlattice,willbeimmobile[1]P.W.Anderson,Phys.Rev.109,1492(1958).

Andersonmodel-IntroductionByP.W.Andersonin1958[1]Andersonmodel-IntroductionIn1983and1984Johnextendedthelocalizationconceptsuccessfullytotheclassicalwaves,suchaselasticwaveandopticalwave[1].Followingthepreviousexperimentalwork,TalSchwartzetal.realizedtheAndersonlocalizationwithdisorderedtwo-dimensionalphotoniclattices[2].[1]JohnS,SompolinskyHandStephenMJ1983Phys.Rev.B275592;JohnSandStephenMJ1983286358;JohnS1984Phys.Rev.Lett.

532169[2]SchwartzTal,BartalGuy,FishmanShmuelandSegev

Mordechai2007Nature

44652Andersonmodel-openproblemsAbrahansetal.’sscalingtheoryforlocalizationin1979[1]（3000citations，oneofthemostimportantpapersincondensedmatterphysics）

Predictions（1）nometal-insulatortransitionin2ddisorderedsystemsSupportedbyexperimentsinearly1980s.

（2）（dephasingtime

）ResultsofJ.J.Linin1987[2]

[1]E.Abrahans,P.W.Anderson,D.C.LicciardelloandT.V.Ramakrisbnan,Phys.Rev.Lett.42,673(1979)[2]J.J.LinandN.Giorano,Phys.Rev.B35,1071(1987);J.J.LinandJ.P.Bird,J.Phys.:Condes.Matter14,R501(2002).

ResultsofJ.J.Linin1987[2]dephasingtimeWorkofHui

Xuetal.onsystemswithcorrelateddisorder:劉小良，徐慧，等，物理學報，55(5)，2493（2006）；劉小良，徐慧，等，物理學報，55(6)，2949（2006）；徐慧,等，物理學報，56(2)，1208（2007）；徐慧,等，物理學報，56(3)，1643（2007）；馬松山，徐慧，等，物理學報，56(5)，5394（2007）；馬松山，徐慧，等，物理學報，56(9)，5394（2007）。Andersonmodel-newpointsofview1。CorrelateddisorderCorrelationanddisorderaretwoofthemostimportantconceptsinsolidstatephysicsPower-lawcorrelateddisorderGaussiancorrelateddisorder2。Entanglement[1]：anindexformetal-insulator,localization-delocalizationtransition”entanglementisakindofunlocalcorrelation”（MPLB19,517,2005）.Entanglementofspinwavefunctions:fourstatesinonesite:0spin;1up;1down;1upand1downEntanglementofspatialwavefunctions(spinlessparticle):twostates:occupiedorunoccupiedMeasuresofentanglement：vonNewmannentropyandconcurrence[1]HaibinLiandXiaoguangWang,Mod.Phys.Lett.B19,517(2005)；Junpeng

Cao,GangXiong,YupengWang,X.R.Wang,Int.J.Quant.Inform.4,705(2006).HefengWangandSabreKais,Int.J.Quant.Inform.4,827(2006).

Andersonmodel-newpointsofview3.newapplications（1）quantumchaos（2）electrontransportinDNAchainsTheimportanceoftheproblemoftheelectrontransportinDNA[1]（3）pentacene[2]（并五苯）MolecularelectronicsOrganicfield-effect-transistorspentacene:layeredstructure,2DAndersonsystem[1]R.G.Endres,D.L.CoxandR.R.P.Singh,Rev.Mod.Phys.76,195(2004)；

StephanRoche,Phys.Rev.Lett.91,108101(2003).[2]M.UngeandS.Stafstrom,SyntheticMetals,139(2003)239-244;J.Cornil,J.Ph.CalbertandJ.L.Bredas,J.Am.Chem.Soc.,123,1520-1521(2001).

DNAstructureEntanglementinone-dimensionalAndersonmodelwithlong-rangecorrelateddisorder

one-dimensionalnearest-neighbortight-bindingmodelConcurrence:vonNeumannentropy

Left.TheaverageconcurrenceoftheAndersonmodelwithpower-lawcorrelationasthefunctionofdisorderdegreeWandforvarious.Abandstructureisdemonstrated.Right.TheaverageconcurrenceoftheAndersonmodelwithpower-lawcorrelationfor=3.0andatthebiggerWrange.Ajumpingfromtheupperbandtothelowerbandisshown

2DentanglementMethod:takingthe2Dlatticeas1Dchain[1]LongyanGongandPeiqingTong,Phys.Rev.E74(2006)056103.；Phys.Rev.A71,042333(2005).

Quantumsmallworldnetworkin[1]squarelatticeLeft.TheaverageconcurrenceoftheAndersonmodelwithpower-lawcorrelationasthefunctionofdisorderdegreeWandforvarious.Abandstructureisdemonstrated.Right.TheaveragevonNewmannentropyoftheAndersonmodelwithpower-lawcorrelationasthefunctionofdisorderdegreeWandforvarious.Abandstructureisdemonstrated.LonczosmethodEntanglementinDNAchainguanine(G),adenine(A),cytosine(C),thymine(T)QusiperiodicalmodelR-Smodeltogeneratethequsiperiodicalsequencewithfourelements(G,C,A,T).Theinflation(substitutions)ruleisG→GC;C→GA;A→TC;T→TA.StartingwithG(thefirstgeneration),thefirstseveralgenerationsareG,GC,GCGA,GCGAGCTC,GCGAGCTCGCGATAGA???.LetFitheelement(site)numberoftheR-Ssequenceintheithgeneration,wehaveFi+1=2Fifori>=1.Sothesitenumberofthefirstseveralgenerationsare1,2,4,8,16,???,andforthe12thgeneration,thesitenumberis2048.TheaverageconcurrenceoftheAndersonmodelfortheDNAchainasthefunctionofsitenumber.Theresultsarecomparedwiththeuncorrelateduniformdistributioncase.

SpinEntanglementofnon-interactingmultipleparticles:Green’sfunctionmethodFinitetemperaturetwobodyGreen’sfunctionOneparticledensitymatrixandOnebodyGreen’sfunctionTwoparticledensitymatrixwhere,HFapprox.

Ifandwhere&whereGeneralizedWernerStatethenInbasisSeparabilitycriterion=PPT=alwayssatisfiedsinceConductanceandmagnetoconductanceoftheAndersonmodelwithlong-rangecorrelateddisorder(1)Staticconductanceofthetwo-dimensionalquantumdotswithlong-rangecorrelateddisorder

Idea:thedistributionfunctionoftheconductanceinthelocalizedregime1d:clearGaussian2d:unclearMethodtocalculatingtheconductance:Green’sfunctionandKuboformulaFig.1Fig.2aFig.2bFig.1ConductanceasthefunctionofFermienergyforthesystemswithpower-lawcorrelateddisorder(W=1.5)forvariousexponent.Ther