Exact expectation values of local fields in quantum sine-Gordon model

TL;DR

This paper derives an explicit formula for vacuum expectation values of exponential fields in the sine-Gordon model, aligning with known semi-classical and perturbative results, and applies it to predict asymptotic behaviors in related quantum spin chains.

Contribution

It provides a new explicit expression for expectation values in the sine-Gordon model, bridging semi-classical and perturbative approaches, and extends these results to quantum spin chain correlations.

Findings

Explicit formula matches semi-classical and perturbative results.

Predicts large-distance asymptotics of two-point functions in XXZ spin chain.

Enhances understanding of correlation functions in integrable quantum field theories.

Abstract

We propose an explicit expression for vacuum expectation values of the exponential fields in the sine-Gordon model. Our expression agrees both with semi-classical results in the sine-Gordon theory and with perturbative calculations in the Massive Thirring model. We use this expression to make new predictions about the large-distance asymptotic form of the two-point correlation function in the XXZ spin chain.