Introduction to the Statistical Physics of Integrable Many-body Systems

Introduction to the Statistical Physics of Integrable Many-body Systems

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Professor Ladislav Šamaj, Professor Zoltán Bajnok
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 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.

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
Yang–Baxter equation
transfer matrix and its diagonalization
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