1．Introduction 1
1.1 Why is the Topic of the Book Worthwhile Studying? 1
1.2 Thermodynamics 5
1.3 Statistical Mechanics:Simple Models 7
1.4 Mermin-Hohenberg Theorem 17
2．uantum Spin-1/2 Chain with the Nearest-Neighbour Couplings 25
2.1 Ohe-Dimensional Spin Hamiltonian 26
2.2 Ising Chain 27
2.3 Isotropic XY Ring 30
2.4 Ising Chain in a Transverse Magnetic Field 35
2.5 Dimerized XY Chain 38
3．Co-ordinate Bethe Ansatz for a Heisenberg-Ising Ring 49
3.1 Bethe Ansatz 49
3.2 Simple Solutions of the Bethe Ansatz Equations:Strings 55
3.3 Thermodynamic Bethe Ansatz 57
3.4 The Ground State Behaviour 62
3.5 Magnetic Field Behaviour in the Ground State:Wiener-Hopf Method 66
4．Correlated Electron Chains:Co-ordinate Bethe Ansatz 73
4.1 Hubbard Chain 74
4.2 t-J Chain 97
5．Algebraic Bethe Ansatz 115
5.1 The Algebraic Bethe Ansatz for a Spin-1/2Chain 115
5.2 SU(2)-Symmetric Spin-S Chain 124
5.3 The Algebraic Bethe Ansatz for Correlated Electron Models 137
6．Correlated Quantum Chains with Open Boundary Conditions 149
6.1 Open Boundaries.XY and Ising Chains 149
6.2 Open Boundaries:Co-ordinate Bethe Ansatz for the Heisenberg-Ising Chain 153
6.3 Open Boundaries.The Algebraic Bethe Ansatz 164
6.4 Open Hubbard Chain 171
6.5 Open Supersymmetric t-J Chain 181
7．Correlated Quantum Chains with Isolated Impurities 189
7.1 Impurities in XY Chains 189
7.2 Impurities in Spin Chains:Bethe Ansatz 200
7.3 Impurity in Correlated Electron Chains 219
8．Correlated Quantum Chains with a Finite Concentration of Impurities 243
8.1 Impurities'Bands 243
8.2 Disodered Ensembles of Impurities in Correlated Chains."Quantum Transfer Matrix"Approach 262
9．Finite Size Corrections in Quantum Correlated Chains 285
9.1 Finite Size Corrections for Quantum Spin Chains 285
9.2 Finite Size Corrections for Correlated Electron Chains 294
9.3 Elements of Conformal Field Theory 304
9.4 Asymptotics of Correlation Functions 316
9.5 Persistent Currents in Correlated Electron Rings 323
10．Beyond the Integrability:Approximate Methods 335
10.1 Scaling Analysis 335
10.2 Bosonization 339
Bibliography 355
Index 365