$Q$-Boson model and relations with integrable hierarchies

TL;DR

This paper explores the connections between the q-boson quantum integrable model and classical integrable hierarchies like Toda and KP, focusing on scalar products, correlation functions, and tau functions.

Contribution

It establishes new links between the q-boson model and classical hierarchies, analyzing scalar products and correlation functions through tau functions and Schur polynomial expansions.

Findings

Scalar products relate to tau functions of integrable hierarchies.

Correlation functions can be expressed via tau functions and Schur polynomials.

The work deepens understanding of quantum-classical integrable system relations.

Abstract

This work investigates the intricate relationship between the q-boson model, a quantum integrable system, and classical integrable systems such as the Toda and KP hierarchies. Initially, we analyze scalar products of off-shell Bethe states and explore their connections to tau functions of integrable hierarchies. Furthermore, we discuss correlation functions within this formalism, examining their representations in terms of tau functions, as well as their Schur polynomial expansions.