Seminarium KMMF "Teoria Dwoistości"

The quantum transfer matrix is an auxiliary tool allowing one to significantly simplify the problem of effectively calculating the the per site free energy as well as the correlation functions of a one dimensional quantum spin chain model at finite temperature. It is conjectured that certain universal features arising in the long-distance asymptotic behaviour of multi-point functions of critical one-dimensional quantum spin chains directly at zero temperature also manifest themselves on the level of the low-temperature behaviour of various quantities related with the associated quantum transfer matrix. In particular, if a given conformal field theory captures the long distance behaviour in the model et zero temperature, than the spectrum of this conformal field theory should arise in the low-temperature behaviour of the spectrum of the quantum transfer matrix.In the case of the XXZ chain spin-1/2 chain, the quantum transfer matrix may be even chosen to be integrable, what allows one, in principle, to study the mentioned universalityproperties of its spectrum by means of the Bethe Ansatz. In this talk, I will describe how the Bethe Ansatz approach can be put on rigorous grounds for the quantum transfer matrixsubordinate to the XXZ chain. Further, I will explain how those results then allow one to access to the universal features of the spectrum of the quantum transfer matrix by showingthat a subset thereof explicitly contains, in the low-temperature limit, the spectrum of the c = 1 free Boson conformal field theory.This is a joint work with S. Faulmann and F. Göhmann.