XXZ scalar products, Miwa variables and discrete KP

TL;DR

This paper demonstrates that the Bethe scalar product in inhomogeneous XXZ spin chains can be represented as a discrete KP tau-function, linking quantum integrable models with classical discrete integrable hierarchies.

Contribution

It establishes a novel connection between Bethe scalar products and discrete KP tau-functions using Miwa variables as rapidities.

Findings

Bethe scalar products are discrete KP tau-functions.

Miwa variables correspond to rapidities of the arbitrary state.

Provides a new integrable systems perspective on XXZ models.

Abstract

We revisit the quantum/classical integrable model correspondence in the context of inhomogeneous finite length XXZ spin-1/2 chains with periodic boundary conditions and show that the Bethe scalar product of an arbitrary state and a Bethe eigenstate is a discrete KP tau-function. The continuous Miwa variables of discrete KP are the rapidities of the arbitrary state.