Introduction to the Statistical Physics of Integrable Many-body Systems
Introduction to the Statistical Physics of Integrable Many-body Systems
Zoltán Bajnok, Hungarian Academy of Sciences, Budapest
£155.00
GBPIncluding 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 Yang–Baxter 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.
- Provides a detailed analysis of a wide range of models of integrable systems, presented in a self-contained way
- Several groups of models of integrable systems are considered, such as the Bose and Fermi gases, basic spin chains and models in condensed matter theory
- Includes a discussion of modern trends in the thermodynamic Bethe ansatz
Product details
May 2013Hardback
9781107030435
523 pages
252 × 171 × 30 mm
1.08kg
29 b/w illus. 113 exercises
Available
Table of Contents
- 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: Yang–Baxter 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.
