Overlaps of Partial Neel States and Bethe States

TL;DR

This paper investigates the overlaps between partial Neel states, which generalize classical antiferromagnetic states, and Bethe states, revealing their connection to boundary domain-wall partition functions and deriving determinant formulas.

Contribution

It introduces a novel approach linking partial Neel and Bethe states to boundary partition functions and provides new determinant representations for these overlaps.

Findings

Overlap expressed as a partial reflecting-boundary domain-wall partition function

Derived determinant formulas for off-shell Bethe states

Derived determinant formulas for on-shell Bethe states

Abstract

Partial Neel states are generalizations of the ordinary Neel (classical anti-ferromagnet) state that can have arbitrary integer spin. We study overlaps of these states with Bethe states. We first identify this overlap with a partial version of reflecting-boundary domain-wall partition function, and then derive various determinant representations for off-shell and on-shell Bethe states.