Surface free energy of the open XXZ spin-1/2 chain    [PDF]

K. K. Kozlowski, B. Pozsgay
We study the boundary free energy of the XXZ spin-\$\tf{1}{2}\$ chain subject
to diagonal boundary fields. We first show that the representation for its
finite Trotter number approximant obtained by Bortz, Frahm and G\"{o}hmann is
related to the partition function of the six-vertex model with reflecting ends.
Building on the Tsuchiya determinant representation for the latter quantity we
are able to take the infinite Trotter number limit. This yields a
representation for the surface free energy which involves the solution of the
non-linear integral equation that governs the thermodynamics of the XXZ
spin-1/2 chain subject to periodic boundary conditions. We show that this
integral representation allows one to extract the low-\$T\$ asymptotic behavior
of the boundary magnetization at finite external magnetic field on the one hand
and numerically plot this function on the other hand.
View original: http://arxiv.org/abs/1201.5884