Surface free energy for systems with integrable boundary conditions

TL;DR

This paper develops a method to compute the surface free energy in integrable quantum systems with boundaries, introducing a new boundary operator for the XXZ spin chain to analyze surface thermodynamics.

Contribution

It presents a novel approach using the quantum transfer matrix formalism and introduces a finite temperature boundary operator for the XXZ chain.

Findings

Expressed surface free energy as a matrix element of projection operators

Introduced a finite temperature boundary operator for the XXZ chain

Provided a framework for analyzing surface thermodynamics in integrable models

Abstract

The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free energy in the thermodynamic limit of systems with integrable boundary conditions as a matrix element of certain projection operators. Specializing to the XXZ spin 1/2 chain we introduce a novel `finite temperature boundary operator' which characterizes the thermodynamical properties of surfaces related to integrable boundary conditions.