Six - Vertex Model with Domain wall boundary conditions. Variable inhomogeneities

TL;DR

This paper investigates the six-vertex model with domain wall boundary conditions, focusing on inhomogeneities derived from Bethe Ansatz solutions, and derives integral formulas for correlation functions including the emptiness formation probability.

Contribution

It introduces a broad class of inhomogeneities based on Bethe Ansatz solutions and provides a generalized integral representation for correlation functions in the six-vertex model.

Findings

Derived multiple integral representation for emptiness formation probability

Extended known formulas for XXZ antiferromagnets to broader inhomogeneity cases

Analyzed arrow correlations for specific inhomogeneity choices

Abstract

We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of inhomogeneities. For certain choices of the inhomogeneities we study arrow correlation functions on the horizontal line going through the centre. In particular we obtain a multiple integral representation for the emptiness formation probability that generalizes the known formul\ae for XXZ antiferromagnets.