The Lieb-Liniger model

TL;DR

This review comprehensively discusses the Lieb-Liniger model, an exactly solvable system of one-dimensional bosons with contact interactions, highlighting exact solutions, relations, and recent advances.

Contribution

It introduces new results on ground-state energy convergence, high-energy excitation spectrum, and boundary energy evaluation within the Lieb-Liniger model.

Findings

Convergence of the ground-state energy series at strong interactions

High-energy excitation spectrum analysis

Evaluation of boundary energy

Abstract

The Lieb-Liniger model describes one-dimensional bosons with contact interactions. This many-body system admits an exact solution in terms of the Bethe ansatz. Some of the exact and perturbative results for this model are reviewed. Particular attention is devoted to the explicit evaluation, in terms of the interaction parameter, of physical quantities that can be formally exactly extracted from the Bethe ansatz solution. Another goal of this review is to stress exact relations between various quantities. The technical developments are explained in detail. The most relevant experimental realisations of the studied problems are eventually discussed. This review also contains several new results such as the study of convergence of the ground-state energy series at strong interactions, the excitation spectrum at high energies, and the evaluation of the boundary energy.