Emptiness formation probability in the domain-wall six-vertex model

TL;DR

This paper calculates the emptiness formation probability in the domain-wall six-vertex model using quantum inverse scattering, providing determinant and integral formulas to understand limit shapes in the model.

Contribution

It introduces a method to compute the emptiness formation probability for the inhomogeneous six-vertex model and derives explicit formulas for the homogeneous case.

Findings

Derived determinant representation of the probability

Obtained multiple integral formula for the homogeneous model

Enhanced understanding of limit shapes in the six-vertex model

Abstract

The emptiness formation probability in the six-vertex model with domain wall boundary conditions is considered. This correlation function allows one to address the problem of limit shapes in the model. We apply the quantum inverse scattering method to calculate the emptiness formation probability for the inhomogeneous model. For the homogeneous model, the result is given both in terms of certain determinant and as a multiple integral representation.