Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle

TL;DR

This paper introduces an integrable lattice discretization of the repulsive delta Bose gas on a ring, solving its spectral problem using Bethe Ansatz and connecting it to Hall-Littlewood polynomials, recovering known continuum results.

Contribution

It presents a novel integrable lattice model for the delta Bose gas and explicitly solves its spectral problem using Bethe Ansatz, linking eigenfunctions to Hall-Littlewood polynomials.

Findings

Eigenfunctions are given by specializations of Hall-Littlewood polynomials.

Spectral problem solved explicitly via Bethe Ansatz.

Continuum limit recovers Lieb-Liniger solution, including orthogonality.

Abstract

We introduce an integrable lattice discretization of the quantum system of n bosonic particles on a ring interacting pairwise via repulsive delta potentials. The corresponding (finite-dimensional) spectral problem of the integrable lattice model is solved by means of the Bethe Ansatz method. The resulting eigenfunctions turn out to be given by specializations of the Hall-Littlewood polynomials. In the continuum limit the solution of the repulsive delta Bose gas due to Lieb and Liniger is recovered, including the orthogonality of the Bethe wave functions first proved by Dorlas (extending previous work of C.N. Yang and C.P. Yang).