NLIE for hole excited states in the sine-Gordon model with two boundaries

TL;DR

This paper derives a nonlinear integral equation for excited states in the sine-Gordon model with boundaries, enabling numerical and analytical analysis of their properties across different scales.

Contribution

The authors develop a new NLIE for bulk excited states in the boundary sine-Gordon model, including boundary terms, and validate it through multiple analytical and numerical methods.

Findings

Numerical computation of state dimensions across scales.

Analytical confirmation of UV and IR limits.

Support for the NLIE via BCPT, BTCSA, and Luscher formula.

Abstract

We derive a nonlinear integral equation (NLIE) for some bulk excited states of the sine-Gordon model on a finite interval with general integrable boundary interactions, including boundary terms proportional to the first time derivative of the field. We use this NLIE to compute numerically the dimensions of these states as a function of scale, and check the UV and IR limits analytically. We also find further support for the ground-state NLIE by comparison with boundary conformal perturbation theory (BCPT), boundary truncated conformal space approach (BTCSA) and the boundary analogue of the Luscher formula.