Spectrum of the quantum transfer matrix of the Heisenberg-Ising chain in the critical regime / Saskia Imke Faulmann. Wuppertal, September 2023
Inhalt
- 1 Introduction
- 2 The quantum transfer matrix formalism
- 2.1 Algebraic Bethe Ansatz and quantum transfer matrix
- 2.2 Auxiliary functions and non-linear integral equations
- 3 Solvability of the non-linear problem
- 3.1 Linear integral equations
- 3.2 Working hypotheses
- 3.3 Existence and uniqueness of solutions to the non-linear problem
- 4 The non-linear integral equation for low temperatures
- 4.1 A contour with better properties
- 4.2 An equivalent non-linear integral equation
- 4.3 The low-temperature expansion of the auxiliary function
- 5 The dressed energy
- 5.1 Properties of kernel and resolvent
- 5.2 Existence and uniqueness of the Fermi point
- 5.3 The dressed energy in the complex plane for 0<< 1
- 5.4 The dressed energy in the complex plane for -1 < < 0
- 5.5 The dressed energy on the curved contour
- 6 Analysis of the quantisation conditions
- 6.1 The solution to the non-linear integral equation in a factorised form
- 6.2 Structure of solutions to the quantisation equations
- 6.3 Conjecture for -1 < < 0
- 7 Low-temperature behaviour of physical observables
- 8 Summary and Outlook
- Appendix
- A Auxiliary Lemmata
- Bibliography