一维和二维关联无序安德森模型.

One-andtwo-dimensionalAndersonmodelwithlong-rangecorrelated-disorder一维和二维关联无序安德森模型One-andtwo-dimensionalAndersonmodelwithlong-rangecorrelated-disorderAndersonmodel-IntroductionEntanglementin1D2DEntanglement2Dconductance2Dtransmission2DmagnetoconductanceAndersonmodel-IntroductionWhatisadisorderedsystem?Nolong-rangetranslationalorderTypesofdisorder(a)crystal(b)Componentdisorder(c)positiondisorder(d)topologicaldisorderdiagonaldisorderoff-diagonaldisordercompletedisorderLocalizationprediction：anelectron,whenplacedinastrongdisorderedlattice,willbeimmobile[1]P.W.Anderson,Phys.Rev.109,1492(1958).jitiiHNijijNiNii11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,FishmanShmuelandSegevMordechai2007Nature44652Andersonmodel-openproblemsAbrahansetal.’sscalingtheoryforlocalizationin1979[1]（3000citations，oneofthemostimportantpapersincondensedmatterphysics）Predictions（1）nometal-insulatortransitionin2ddisorderedsystemsSupportedbyexperimentsinearly1980s.（2）（dephasingtime）ResultsofJ.J.Linin1987[2]0T[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).0TcResultsofJ.J.Linin1987[2]dephasingtimeWorkofHuiXuetal.onsystemswithcorrelateddisorder:刘小良，徐慧，等，物理学报，55(5)，2493（2006）；刘小良，徐慧，等，物理学报，55(6)，2949（2006）；徐慧,等，物理学报，56(2)，1208（2007）；徐慧,等，物理学报，56(3)，1643（2007）；马松山，徐慧，等，物理学报，56(5)，5394（2007）；马松山，徐慧，等，物理学报，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)；JunpengCao,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-rangecorrelateddisorderone-dimensionalnearest-neighbortight-bindingmodelConcurrence:]1)[(121NiiMCijijiiijtEvonNeumannentropy0ncn011nNnnNnncn00)1(11nnnnnnnzz)1(log)1(log22nnnnvnzzzzENnvnvENE1134567890.020.040.060.080.100.120.140.160.18C(10-4)W1.51.72.02.052.13.03.54.05.0power-lawcorrelated91011121314150.010.020.030.040.050.060.070.08C(10-4)Wpower-lawcorrelatedLeft.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]squarelattice051015200.00.51.01.52.02.53.03.5C(10-4)W1.752.02.53.54.04.55.5L=30051015200.20.30.40.50.60.7vonNeumannentropyW1.752.02.53.54.04.55.5L=30Left.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,t