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Spectrum of the quantum transfer matrix of the Heisenberg-Ising chain in the critical[...]
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
7.1 Low-temperature behaviour of particle and hole roots
7.2 The eigenvalues for low temperatures
8 Summary and Outlook
Appendix
A Auxiliary Lemmata
Bibliography
Dissertation
Spectrum of the quantum transfer matrix of the Heisenberg-Ising chain in the critical regime / Saskia Imke Faulmann
Entstehung
Wuppertal
September 2023
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