Introduction to the Statistical Physics of Integrable Many-body Systems

Including topics not traditionally covered, such as (1+1)-dimensional QFT, this book considers a wide range of models and their applications.

Ladislav Šamaj (Author), Zoltán Bajnok (Author)

9781107030435, Cambridge University Press

Hardback, published 16 May 2013

523 pages, 29 b/w illus. 113 exercises
25.2 x 17.1 x 3 cm, 1.08 kg

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 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.

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.

Subject Areas: Mathematical physics [PHU], Statistical physics [PHS], Physics [PH], Mathematics & science [P]