Comments on Slavnov products, Temperley-Lieb open spin chains, and KP tau functions

TL;DR

This paper explores the connection between Slavnov's inner products in open Temperley-Lieb chains and the KP hierarchy, revealing that for the s=1/2 XXZ spin chain, these products relate to tau functions and involve Schur polynomial expansions.

Contribution

It demonstrates that Slavnov products for the s=1/2 XXZ chain can be expressed as quotients of tau functions, linking quantum integrable models with KP hierarchy structures.

Findings

Slavnov products are related to KP tau functions for s=1/2 XXZ chains.

Schur polynomial expansions are used to analyze these products.

A matrix construction for Baker-Akhiezer functions is introduced.

Abstract

We study Slavnov's inner products for open Temperley-Lieb chains and their relations with the KP hierarchy. We show that when (s=1/2) the quantum group invariant XXZ spin chain has Slavnov products given by the quotient of tau functions. The Schur polynomials expansion and a matrix construction for the Baker-Akhiezer functions are also briefly considered.