Finite Size Effects In Correlated Electron Models: Exact Results

by ZVYAGIN, ANDREI A.

• ISBN13: 9781860945038
• ISBN10: 1860945031
• Format: Hardcover
• Copyright: 2005-05-25
• Publisher: Textstream

Summary

- Describes features of the Bethe Ansatz methods in a compact, unified and self-contained manner- Discusses other popular methods such as conformal field theory, scaling and bosonization, which have not previously been studied- Presents a number of original results for models of physics of popular correlated electron systems

Table of Contents

Preface	vii
1. Introduction	1	(24)
1.1 Why is the Topic of the Book Worthwhile Studying?	1	(4)
1.2 Thermodynamics	5	(2)
1.3 Statistical Mechanics: Simple Models	7	(10)
1.4 Mermin-Hohenberg Theorem	17	(8)
2. Quantum Spin-½ Chain with the Nearest-Neighbour Couplings	25	(24)
2.1 One-Dimensional Spin Hamiltonian	26	(1)
2.2 Ising Chain	27	(3)
2.3 Isotropic XY Ring	30	(5)
2.4 Ising Chain in a Transverse Magnetic Field	35	(3)
2.5 Dimerized XY Chain	38	(11)
3. Co-ordinate Bethe Ansatz for a Heisenberg-Ising Ring	49	(24)
3.1 Bethe Ansatz	49	(6)
3.2 Simple Solutions of the Bethe Ansatz Equations: Strings	55	(2)
3.3 Thermodynamic Bethe Ansatz	57	(5)
3.4 The Ground State Behaviour	62	(4)
3.5 Magnetic Field Behaviour in the Ground State: Wiener-Hopf Method	66	(7)
4. Correlated Electron Chains: Co-ordinate Bethe Ansatz	73	(42)
4.1 Hubbard Chain	74	(23)
4.2 t-J Chain	97	(18)
5. Algebraic Bethe Ansatz	115	(34)
5.1 The Algebraic Bethe Ansatz for a Spin-½ Chain	115	(9)
5.2 SU(2)-Symmetric Spin-S Chain	124	(13)
5.3 The Algebraic Bethe Ansatz for Correlated Electron Models	137	(12)
6. Correlated Quantum Chains with Open Boundary Conditions	149	(40)
6.1 Open Boundaries. XY and Ising Chains	149	(4)
6.2 Open Boundaries: Co-ordinate Bethe Ansatz for the Heisenberg-Ising Chain	153	(11)
6.3 Open Boundaries. The Algebraic Bethe Ansatz	164	(7)
6.4 Open Hubbard Chain	171	(10)
6.5 Open Supersymmetric t-J Chain	181	(8)
7. Correlated Quantum Chains with Isolated Impurities	189	(54)
7.1 Impurities in XY Chains	189	(11)
7.2 Impurities in Spin Chains: Bethe Ansatz	200	(19)
7.3 Impurity in Correlated Electron Chains	219	(24)
8. Correlated Quantum Chains with a Finite Concentration of Impurities	243	(42)
8.1 Impurities' Bands	243	(19)
8.2 Disodered Ensembles of Impurities in Correlated Chains. "Quantum Transfer Matrix" Approach	262	(23)
9. Finite Size Corrections in Quantum Correlated Chains	285	(50)
9.1 Finite Size Corrections for Quantum Spin Chains	285	(9)
9.2 Finite Size Corrections for Correlated Electron Chains	294	(10)
9.3 Elements of Conformal Field Theory	304	(12)
9.4 Asymptotics of Correlation Functions	316	(7)
9.5 Persistent Currents in Correlated Electron Rings	323	(12)
10. Beyond the Integrability: Approximate Methods	335	(20)
10.1 Scaling Analysis	335	(4)
10.2 Bosonization	339	(16)
Bibliography	355	(10)
Index	365