Abstract
We study the boundary free energy of the XXZ spin-1/2 chain subject to diagonal boundary fields. We first show that the representation for itsfinite Trotter number approximant obtained by Göhmann, Bortz and Frahm is related to thepartition function of the six-vertex model with reflecting ends. Building on the Tsuchiyadeterminant representation for the latter quantity we are able to take the infinite Trotternumber limit. This yields a representation for the surface free energy which involves thesolution of the non-linear integral equation that governs the thermodynamics of the XXZ spin-1/2 chainsubject to periodic boundary conditions. We show that this integral representation allows one to extractthe low-T asymptotic behavior of the boundary magnetization at finite external magnetic field on theone hand and numerically plot this function on the other hand.
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