Models of Quantum Matter A First Course on Integrability and the Bethe Ansatz

Hans-Peter Eckle, Adjunct Professor, Humboldt Study Centre, Ulm University, Germany

Hans-Peter Eckles is Adjunct Professor at Ulm University. His research is focused on exactly solvable and integrable models of strongly interacting quantum systems, especially quantum optical models in collaboration with University of Gothenburg, Sweden. He organises and teaches at summer schools in Ireland and Turkey, and is involved with the development and teaching of courses in philosophy of science and research ethics at Ulm University and invited courses on research ethics (e.g. in Aachen, Berlin, Dresden, Freiburg, Gottingen, and Konstanz).
Previously, he has taught and conducted research in theoretical physics at Princeton University, University of Arizona, USA, Australian National University and University of New South Wales, Sydney, University, Universities of Tours and Nancy, France, University of Gothenburg, Sweden, University of Jyvaskyla, Finland, and University of Hannover and Free University Berlin, Germany.

1. Historical Remarks
2. Introduction
PART I: General Preliminaries
3. Many-particle systems
4. Angular momentum
5. Statistical mechanics
Part II: Special Preliminaries
6. Models of magnetism
7. Electronic models
8. Nonlinear quantum optics
9. Cold atoms and optical lattices
10. Quantum entanglement
11. Quantum impurities
12. Quantum groups
13. Models of non-equilibrium statistical mechanics
PART III: Algebraic Bethe ansatz
14. Ice model
15. General vertex models
16. Six-vertex model
PART IV: Coordinate Bethe ansatz
17. Introduction
18. The anisotrpic spin chain
19. Bethe ansatz for the XXZ spin chain
PART V: Review of further Bethe ansatz models
20. Bose gas
21. Exactly solvable quantum optical models
PART VI: Multicomponent systems: Nested Bethe ansatz
24. Multicomponent systems
25. Examples
26. Fermi gas
27. Hubbard model
28. Magnetic impurity models
29. Kondo Model
PART VII: Thermodynamics Bethe ansatz
30. Introduction
31. Main idea
32. Thermodynamics
PART VIII: Critical phenomena, finite-size scaling and conformal invariance
33. Introduction
34. Critical phenomena
35. Finite-size scaling
36. Conformal invariance
PART IX: Bethe ansatz for finite systems
37. Introduction
38. Euler-Maclaurin formula
39. Wiener-Hopf technique
40. Finite Heisenber quantum spin chain
PART X: Suggested further reading
41. General preliminaries
42. Speical preliminaries
43. Algebraic Bethe ansatz
44. Cooredinate Bethe ansatz
45. Thermodynamic Bethe ansatz
46. Conformal invariance and finite-size scaling
47. Bethe ansatz for finite systems
48. General reading list