Bi-partite entanglement entropy in integrable models with backscattering

TL;DR

This paper extends the understanding of bi-partite entanglement entropy in integrable quantum field theories to models with backscattering, showing the leading correction depends only on the mass spectrum, not on scattering details.

Contribution

It generalizes previous results to models with non-diagonal scattering matrices, demonstrating the infrared correction form is unchanged by backscattering effects.

Findings

Infrared correction form is identical for models with and without backscattering.

Detailed analysis of the sine-Gordon model confirms the correction in the large distance regime.

Leading correction to the sine-Gordon partition function is obtained without bound states.

Abstract

In this paper we generalise the main result of a recent work by J. L. Cardy and the present authors concerning the bi-partite entanglement entropy between a connected region and its complement. There the expression of the leading order correction to saturation in the large distance regime was obtained for integrable quantum field theories possessing diagonal scattering matrices. It was observed to depend only on the mass spectrum of the model and not on the specific structure of the diagonal scattering matrix. Here we extend that result to integrable models with backscattering (i.e. with non-diagonal scattering matrices). We use again the replica method, which connects the entanglement entropy to partition functions on Riemann surfaces with two branch points. Our main conclusion is that the mentioned infrared correction takes exactly the same form for theories with and without backscattering. In order to give further support to this result, we provide a detailed analysis in the sine-Gordon model in the coupling regime in which no bound states (breathers) occur. As a consequence, we obtain the leading correction to the sine-Gordon partition function on a Riemann surface in the large distance regime. Observations are made concerning the limit of large number of sheets.