On the NLIE of (inhomogeneous) open spin-1 XXZ chain with general integrable boundary terms

TL;DR

This paper derives nonlinear integral equations for the inhomogeneous open spin-1 XXZ chain with general boundary conditions, enabling the computation of boundary and Casimir energies, and the effective central charge in the UV limit.

Contribution

It introduces a new derivation of NLIEs for the open spin-1 XXZ chain with general boundary terms, extending previous diagonal boundary analyses.

Findings

Derived NLIEs for inhomogeneous open spin-1 XXZ chain

Computed boundary and Casimir energies of the supersymmetric sine-Gordon model

Obtained analytical expression for the effective central charge in the UV limit

Abstract

Starting from the T-Q equations of the open spin-1 XXZ quantum spin chain with general integrable boundary terms, for values of the boundary parameters which satisfy a certain constraint, we derive a set of nonlinear integral equations (NLIEs) for the inhomogeneous open spin-1 XXZ chain. By taking the continuum limit of these NLIEs, and working in analogy with the open spin-1 XXZ chain with diagonal boundary terms, we compute the boundary and the Casimir energies of the corresponding supersymmetric sine-Gordon (SSG) model. We also present an analytical result for the effective central charge in the ultraviolet (UV) limit.