Exact Matrix Elements of the Field Operator in the Thermodynamic Limit of the Lieb-Liniger Model

TL;DR

This paper derives exact expressions for the matrix elements of the field operator in the Lieb-Liniger model in the thermodynamic limit, providing a precise analytical tool for understanding quantum many-body systems with delta interactions.

Contribution

It introduces a novel method combining Bethe ansatz and Slavnov determinants to compute exact matrix elements for any coupling constant in the thermodynamic limit.

Findings

Exact matrix elements obtained for all coupling constants

Results agree with semiclassical limits as c approaches zero

Provides a new analytical approach for quantum integrable models

Abstract

We study a matrix element of the field operator in the Lieb-Liniger model using the Bethe ansatz technique coupled with a functional approach to compute Slavnov determinants. We obtain the matrix element exactly in the thermodynamic limit for any coupling constant $c$, and compare our results to known semiclassics at the limit $c\to0.$