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 universality
properties 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 matrix
subordinate 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 showing
that 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.