Exact surface energy and helical spinons in the XXZ spin chain with arbitrary non-diagonal boundary fields

TL;DR

This paper introduces an analytic method to compute surface energy and elementary excitations in the XXZ spin chain with arbitrary non-diagonal boundary fields, revealing boundary correlation effects and spinon-like excitations.

Contribution

The paper presents a universal analytic approach for calculating surface energy and excitations in integrable systems with or without U(1) symmetry, including boundary effects.

Findings

Boundary contributions to surface energy are non-additive in the gapped case under certain parameters.

In the gapless case, boundary contributions are additive due to lack of long-range correlations.

Exact spinon-like excitations are observed despite broken U(1) symmetry.

Abstract

An analytic method is proposed to compute the surface energy and elementary excitations of the XXZ spin chain with generic non-diagonal boundary fields. For the gapped case, in some boundary parameter regimes the contributions of the two boundary fields to the surface energy are non-additive. Such a correlation effect between the two boundaries also depends on the parity of the site number $N$ even in the thermodynamic limit $N\to\infty$. For the gapless case, contributions of the two boundary fields to the surface energy are additive due to the absence of long-range correlation in the bulk. Although the $U(1)$ symmetry of the system is broken, exact spinon-like excitations, which obviously do not carry spin-$\frac12$, are observed. The present method provides an universal procedure to deal with quantum integrable systems either with or without $U(1)$ symmetry.