Quantum Phase Transitions.pdf

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1、QUANTUMPHASETRANSITIONSSUBIRSACHDEVProfessorofPhysics,YaleUniversity,NewHaven,CT06520-8120,USAOctober13,1998TobepublishedbyCambridgeUniversityPress.ToMenaka,MonishaandUshaContentsPrefacepagexiAcknowledgementsxvPartone:Introduction11Basicconcepts31.1Whatisaquantumphasetran

2、sition?31.2Quantumversusclassicalphasetransitions61.3Experimentalexamples81.4Theoreticalmodels101.4.1QuantumIsingmodel101.4.2Quantumrotormodel132Themappingtoclassicalstatisticalmechanics:singlesitemodels172.1TheclassicalIsingchain182.1.1Thescalinglimit212.1.2Universality2

3、22.1.3Mappingtoaquantummodel:Isingspininatransverseeld232.2TheclassicalXYchainandaO(2)quantumrotor262.3TheclassicalHeisenbergchainandaO(3)quantumrotor333Overview363.1Quantumeldtheories403.2What'sdierentaboutquantumtransitions?44Parttwo:QuantumIsingandRotorModels494TheI

4、singchaininatransverseeld514.1LimitingcasesatT=0544.1.1Strongcouplingg1554.1.2Weakcouplingg1604.2Exactspectrum614.3Continuumtheoryandscalingtransformations64vviContents4.4Equaltimecorrelationsoftheorderparameter724.5Finitetemperaturecrossovers754.5.1LowTonthemagnetical

5、lyorderedside,
>0,T
784.5.2LowTonthequantumparamagneticside,
<0,Tj
j854.5.3ContinuumHighT,Tj
j924.5.4Summary1004.6Applicationsandextensions1025Quantumrotormodels:largeNlimit1045.1Limitingcases1065.1.1Strongcouplingeg11065.1.2Weakcoupling,ge11095.2Continuumtheoryandla

6、rgeNlimit1115.3Zerotemperature1145.3.1Quantumparamagnet,g>g115c5.3.2Criticalpoint,g=g117c5.3.3Magneticallyorderedgroundstate,gg,T
129c+5.4.2HighT,T

130+;5.4.3LowTonthemagneticallyorderedside,g

7、
130c;5.5Applicationsandextensions1326Thed=1,O(N3)rotormodels1356.1Scalinganalysisatzerotemperature1376.2Lowtemperaturelimitofcontinuumtheory,T
140+6.3Hightemperaturelimitofcontinuumtheory,
TJ147+6.3.1Field-theoreticrenormalizationgroup1506.3.2Computationof154u6.3.3D

8、ynamics1556.4Summary1616.5Applicationsandextensions1617Thed=2,O(N3)rotormodels1647.1LowTonthema