Exact finite volume expectation values of $\bar{\Psi} \Psi$ in the Massive Thirring model from light-cone lattice correlators

TL;DR

This paper computes exact finite volume expectation values of the fermionic operator in the Massive Thirring Model using light-cone lattice regularization, confirming previous conjectures and connecting lattice correlators with NLIE results.

Contribution

It provides the first exact lattice-based computation of these expectation values and verifies their consistency with NLIE and LeClair-Mussardo series predictions.

Findings

Agreement between lattice correlator calculations and NLIE results

Validation of LeClair-Mussardo series conjectures for these expectation values

Explicit finite volume expectation values for ar{\u03a8}Psi} in the Massive Thirring Model

Abstract

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator $\bar{\Psi}\Psi$ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator $\bar{\Psi}\Psi$ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.