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

Technical aspects of bosonization、A simple case of Bose-Fermi equivalence： Jordan-Wigner、Transformation、One-dimensional fermion States 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等等。