Six-vertex model on a finite lattice: integral representations for nonlocal correlation functions

TL;DR

This paper develops integral representations for correlation functions in the six-vertex model with domain wall boundary conditions, providing new formulas for the emptiness formation probability and exploring their mathematical relations.

Contribution

It introduces three integral representations for off-shell Bethe states and derives new integral formulas for correlation functions, including a novel expression for the emptiness formation probability.

Findings

Reproduces known results for emptiness formation probability

Derives new integral representation for correlation functions

Establishes identities relating different integral representations

Abstract

We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum inverse scattering method, we derive three different integral representations for these states. By suitably combining such representations, and using certain antisymmetrization relation in two sets of variables, it is possible to derive integral representations for various correlation functions. In particular, focusing on the emptiness formation probability, besides reproducing the known result, obtained by other means elsewhere, we provide a new one. By construction, the two representations differ in the number of integrations and their equivalence is related to a hierarchy of highly nontrivial identities.