One-particle dynamical correlations in the one-dimensional Bose gas

TL;DR

This paper computes the momentum- and frequency-dependent one-body correlation function of the 1D Lieb-Liniger Bose gas using Algebraic Bethe Ansatz, providing high-accuracy numerical results across various interaction strengths.

Contribution

It introduces a determinant representation for the field form factor suitable for numerical evaluation and reconstructs the correlation function for large systems.

Findings

Accurate correlation functions obtained for various interaction parameters.

Determinant representation facilitates efficient numerical evaluation.

Results include detailed analysis of static and dynamic correlations.

Abstract

The momentum- and frequency-dependent one-body correlation function of the one-dimensional interacting Bose gas (Lieb-Liniger model) in the repulsive regime is studied using the Algebraic Bethe Ansatz and numerics. We first provide a determinant representation for the field form factor which is well-adapted to numerical evaluation. The correlation function is then reconstructed to high accuracy for systems with finite but large numbers of particles, for a wide range of values of the interaction parameter. Our results are extensively discussed, in particular their specialization to the static case.