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Exceptional Seminar Salvish au:Goomanee'><span class='hl'>Salvish</span> Goomanee (ENS Lyon)
In this talk I will present the novel developments pertaining the the thermodynamics of the XXZ spin-1/2 chain. I will describe the analysis allowing one to prove several features related to the behaviour of the Heisenberg-Ising (or XXZ) spin-1/2 chain at finite temperature. It has been argued in the literature that the per-site free energy or the correlation length admit integral representations whose integrands are expressed in terms of solutions of non-linear integral equations. The derivations of such representations rested on various unproven conjectures such as the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the existence and uniqueness of the solutions to the auxiliary non-linear integral equations in the infinite Trotter limit. I will show how these conjectures can be proven in a rigorous setting for temperatures high enough. The result of these analyses allowed one to observe that a subset of sub-dominant Eigenvalues of the quantum transfer matrix admits a large temperature asymptotic expansion.