# Introduction to the Statistical Physics of Integrable Many-body Systems

Cambridge University Press, 5/16/2013

EAN 9781107030435, ISBN10: 1107030439

Hardcover, 523 pages, 24.7 x 17.4 x 3 cm

Language: English

Including topics not traditionally covered in literature, such as (1+1)-dimensional QFT and classical 2D Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. Beginning with a treatise of nonrelativistic 1D continuum Fermi and Bose quantum gases of identical spinless particles, the book describes the quantum inverse scattering method and the analysis of the related YangÃ¢â‚¬â€œBaxter equation and integrable quantum Heisenberg models. It also discusses systems within condensed matter physics, the complete solution of the sine-Gordon model and modern trends in the thermodynamic Bethe ansatz. Each chapter concludes with problems and solutions to help consolidate the reader's understanding of the theory and its applications. Basic knowledge of quantum mechanics and equilibrium statistical physics is assumed, making this book suitable for graduate students and researchers in statistical physics, quantum mechanics and mathematical and theoretical physics.

Preface

Part I. Spinless Bose and Fermi Gases

1. Particles with nearest-neighbour interactions

Bethe ansatz and the ground state

2. Bethe ansatz

zero-temperature thermodynamics and excitations

3. Bethe ansatz

finite-temperature thermodynamics

4. Particles with inverse-square interactions

Part II. Quantum Inverse Scattering Method

5. QISM

YangÃ¢â‚¬â€œBaxter equation

6. QISM

transfer matrix and its diagonalization

7. QISM

treatment of boundary conditions

8. Nested Bethe ansatz for spin-1/2 fermions with delta interactions

9. Thermodynamics of spin-1/2 fermions with delta interactions

Part III. Quantum Spin Chains

10. Quantum Ising chain in a transverse field

11. XXZ Heisenberg chain

Bethe ansatz and the ground state

12. XXZ Heisenberg chain

ground state in the presence of magnetic field

13. XXZ Heisenberg chain

excited states

14. XXX Heisenberg chain

thermodynamics with strings

15. XXZ Heisenberg chain

thermodynamics without strings

16. XYZ Heisenberg chain

17. Integrable isotropic chains with arbitrary spin

Part IV. Strongly Correlated Electrons

18. Hubbard model

19. Kondo effect

20. Luttinger many-fermion model

21. Integrable BCS superconductors

Part V. Sine-Gordon Model

22. Classical sine-Gordon theory

23. Conformal quantization

24. Lagrangian quantization

25. Bootstrap quantization

26. UV-IR relation

27. Exact finite volume description from XXZ

28. Two-dimensional Coulomb gas

Appendix A. Spin and spin operators on chain

Appendix B. Elliptic functions

References

Index.