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1、QuantumCondensedMatterPhysicsChetanNayakMicrosoftStationQUniversityofCaliforniaatSantaBarbaraNovember5,2011iiiThelarge-scalepropertiesofmatteraredescribedbycontinuumquan-tumfieldtheories.Thisbookdealswiththeaimsandmethodsofsuchadescription.Inequilibrium,mattermanifestsitselfin
2、oneofacornucopiaofphasesor,inspecialcircumstances,atatransitionpointbetweentwoormorephases.Thephysicalpropertiesofmatterremainqualitativelythesamewithinanyphase;thesegrosssignaturesaredeterminedbytherobustpropertiesofthephase.Quantumfieldtheoryisamathematicalapparatuswhichcodi
3、fiesthesepropertiesandallowsustomakequantitativecalcula-tionsofthemwhichcanbecomparedwithexperiment.Manyofthelarge-scalepropertiesofasystemaredeterminedbythewaysinwhichitcanbeexcitedbyexternalprobesatrelativelylong-wavelengthsandlow-frequencies.Thelong-wavelength,low-energyexc
4、itationsofasys-temare,inturn,characteristicfeaturesofthestatesofmatterwhichitrealizes.TheknowntypesofsuchexcitationsareGoldstonemodes,gaugefields,localizedexcitations,andcriticalfluctuations.Goldstonemodes,suchasphononsandspinwaves,areanecessaryconcomitantofspontaneouslybrokenc
5、ontinuoussymmetries.Inabrokensymmetry-phase,thegroundstateofthesystemisnotinvariantundersomesymmetryoftheHamilto-nian.Forinstance,acrystalisnottranslationallyinvariantalthoughtheelectron-ionHamiltonianis.Similarly,thegroundstateofamagnethasapreferreddirection–thedirectioninwh
6、ichthemagneticmomentpoints–eventhoughtheunderlyingmicroscopicequationsdonot.Suchstatesarerigidbecauseitisenergeticallyfavorableforthesymmetrytobebrokeninthesamewayindifferentpartsofthesystem.Whenthesymmetryinquestioniscontinuous,suchastranslationalorrotationalsymmetry,thenitis
7、possibletoslowlyvarythedirectionofsymmetry-breakingacrossthesystem,therebycreatingalong-wavelength,low-energyexcitation–aGold-stonemode.Gaugefieldsoccurintopological(or‘fractionalized’)phases.Inthesephases,asystemofstrongly-correlatedelectrons(or,inprinciple,someotherunderlyin
8、gfundamentalconstituent)supportsexcitationswhichhavethequantumnumber