A note on a boundary sine-Gordon model at the free-Fermion point

TL;DR

This paper analyzes the boundary sine-Gordon model at the free-Fermion point, deriving Casimir energy and effective central charge, and confirms results through T-Q equations and TBA approach.

Contribution

It provides an analytical calculation of Casimir energy and effective central charge at the free-Fermion point using auxiliary functions from T-Q equations.

Findings

Casimir energy matches TBA results.

Effective central charge verified in UV limit.

Analytical expressions derived for boundary sine-Gordon model.

Abstract

We investigate the free-Fermion point of a boundary sine-Gordon model with nondiagonal boundary interactions for the ground state using auxiliary functions, obtained from T-Q equations of a corresponding inhomogeneous open spin-1/2 XXZ chain with nondiagonal boundary terms. In particular, we obtain the Casimir energy. Our result for the Casimir energy is shown to agree with the result from the TBA approach. The analytical result for the effective central charge in the ultraviolet (UV) limit is also verified from the plots of effective central charge for intermediate values of volume.