Diagonal multi-soliton matrix elements in finite volume

TL;DR

This paper proposes a conjecture for diagonal matrix elements of local operators in finite volume sine-Gordon models, extending previous results and confirmed through numerical methods, with implications for finite temperature correlators.

Contribution

It extends the finite volume formula for diagonal matrix elements to models with non-diagonal scattering and confirms it numerically.

Findings

The conjecture accurately predicts finite volume dependence of matrix elements.

Numerical results support the conjecture's validity.

The formula can be applied to compute finite temperature correlation functions.

Abstract

We consider diagonal matrix elements of local operators between multi-soliton states in finite volume in the sine-Gordon model, and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Tak\'acs which were only valid for diagonal scattering. In order to test the conjecture we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.