Determinant representation for a quantum correlation function of the lattice sine-Gordon model

TL;DR

This paper develops a determinant representation for correlation functions in a lattice sine-Gordon model, linking it to integrable equations and Riemann Hilbert problems to analyze asymptotic behavior.

Contribution

It introduces a novel determinant formula for lattice sine-Gordon correlation functions and connects it to integrable systems and RHP analysis.

Findings

Determinant representation for lattice sine-Gordon correlation functions.

Asymptotic behavior described via Riemann Hilbert problem.

Leading asymptotic term explicitly obtained.

Abstract

We consider a completely integrable lattice regularization of the sine-Gordon model with discrete space and continuous time. We derive a determinant representation for a correlation function which in the continuum limit turns into the correlation function of local fields. The determinant is then embedded into a system of integrable integro-differential equations. The leading asymptotic behaviour of the correlation function is described in terms of the solution of a Riemann Hilbert Problem (RHP) related to the system of integro-differential equations. The leading term in the asymptotical decomposition of the solution of the RHP is obtained.