玻色化和强关联系统

Preface
Acknowledgements
Part I： Technical aspects of bosonization
A simple case of Bose-Fermi equivalence： Jordan-Wigner ransformation
One-dimensional fermion tates near the Fermi points
Chiral anomaly
Anomalous commutators
Ganssian model. Lagrangian formulation
Bosonization
Interaction with an electromagnetic field; gauge invariance
Conformal symmetry and finite size effects
Gaussian model in the Hamiltonian formulation
Virasoro algebra
Ward identities
Subalgebra sl(2)
Structure of Hilhert space in conformal theories
Differential equations for correlation functions
Dotsenko——Fateev bosonization scheme for the minimal models
Current (Kac-Moody) algebras; the first assault
Sugawara Hamiltonian for Wess-Zumino-Novikov-Witten model
Knizhnik-Zamolodchikov (KZ) equations
Relevant and irrelevant fields
Bose-Einstein Condensation in two dimensions; Beresinskii-
Kesterlitz-Thouless transition
The sine-Gordon model
The renormalization group analysis
Exact solution of the sine-Gordon model
Spin S-1/2 Heisenberg-lsing chain
Explicit expression for the dynamical magnetic susceptibility
Ising model
More about the WZNW model
Special cases
1.1 SU1(2) WZNW model as a Gaussian model
1.2 SU2(2) WZNW model and the Ising model
1.3 SU4(2) as a theory of two bosonic fields
1.4 SUI0(2) as a theory of three bosonic fields
Deformation of the WZNW model and coset constructions
Non-Abelian bosznization
WZNW model in the Lagrangian formulation
Derivation of the Lagrangian
Calculation of a nontrivial determinant
Part II： Application of the bosonization technique to physical models
in (1 + l)-dimemions
Interacting fermions with spin
Spin-l/2 Tomonaga-Luttinger liquid
Instabilities of a Tomonaga-Lnttinger liquid
Electron-phonon interaction
1.1 Incommensurate band filling， the effect on K
1.2 Commensurate band filling
1.3 Appendix
Spectral gap in the spin sector
Optical conductivity
Gap in the charge sector at half-filling and the case of small doping
Appendix. RG equations for the model of one-dimensional electrons
from the SU(2) current algebra
Interacting fermions with broken spin rotational symmetry
U(l)-symmetric Thirring model： relation to sine-Gordon and
massive Thirring models
XYZ Thirring model
Spin correlation functions
Theroleofmagneticfield
IV.ISpin-floptransitionintheXYZmodel
IV.2Toymodelforanorbitalantfferromagnet
WhatmayhappenwithaTomonaga-Luttingerfiquidinthree imensions
Appendix.FermionicGreensfunction
1.1 oordinatespaceGreensfunction
1.2 hespectralfunction(vc>vs)
1.3 ouriertransformoftheGreensfunction(re>v)
1.4 hespectralfunction，vs>vc
1.5 ouriertransformofGreensfunction，vs>vc
TwoweaklycoupledTomonaga-Luttingerliquids;spinlemcase
Spinliquidsinonedimension：exampleofspinladders
Couplingofidenticalchains;theAbelianbosonization
Correlationfunctionsfortheidenticalchains
II.lStaggeredsusceptibilityoftheconventional(Haldane)spin iquid
II.2Dimerizedspinliquid
Inequivalentchains;non-Abelianbosonization
Stringorderparameterinthespin-laddermodel
AppendixA.Thetopologicaltermemergingfromthe
Wess-Zuminoterm
AppendixB.HiddenZ2～Z2symmetryandstringorderparameter
inthebond-alternatingS——-1/2Heisenbergchain
Spin-l/2Heisenbergchainwithalternatingexchange
Appendix.Multiparticleformfactors
Superconductivityinadopedspinliquid
Bosonizationandfermionization
Superconductingfluctuations
Conclusions
Appendix.Conditionsforsuppressionofthesingle-particletunneling
EdgestatesinthequantumHalleffect
PartⅢ Singleimpurityproblems
Potentialsattering
Introduction
Reduction of the local scattering problem to one dimension
The scattering phase
X-ray edge problem (Fermi liquids)
Introduction
Statement of the problem
II.1 Many-body formulation
I1.2 One-particle formulation
Linked dusters expansion
Nozi6res-De Dominicis solution
Exact solution for the overlap integral
Bosonization approach to the X-ray edge problem
VI.1 Boundary condition changing operator (chiral anomaly)
VI.2 X-ray response functions via bosonization
Appendix A. Parquet approximation
Appendix B. The Wiener-Hopf method
Appendix C. Orthogonality of Slater determinants
Impurities in a Tomonaga-Luttinger liquid
Introduction
Weak-coupling analysis of a single impurity
II.1 Bosonization of the impurity Hamiltonian
II.2 Lagrangian formulation： local action
11.3 Renormalization group analysis of local operators
Strong-coupling analysis
III.1 Open boundary bosonization
111.2 Strong-coupling fixed point
Exact solution at K=1/2 and the conductance
Relation of the impurity backscattering model to the Caldeira-eggett model
X-ray edge problem in Tomonaga-Luttinger liquids
Multi-channel Kondo problem
Introduction
Qualitative analysis
The Toulouse limit
The Emery-Kivelson solution
IV.I Greens functions and zero-field free energy
IV.2 Magnetic field effects
IV.3 Wilson ratio
The Toulouse limit for the four-channel Kondo model
Coulomb blockade
VI.1 One-dimensional electrons in point contacts
VI.2 Coulomb blockade and two-channel Kondo model
General bibliography