# Surface free energy of the open XXZ spin-1/2 chain

Source: [Surface free energy of the open XXZ spin-1/2 chain](<https://www.sota2.com/research/paper/68fa30271e209131ce872f34>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T18:02:40.943Z

Authors: K. K. Kozlowski, B. Pozsgay

Published: 2012-01-27T20:40:40.000Z

## Abstract

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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1201.5884>)

[PDF](<https://arxiv.org/pdf/1201.5884.pdf>)