Dynamic and static density-density correlations in the one-dimensional Bose gas: exact results and approximations

TL;DR

This paper presents approximate formulas for the dynamic and static structure factors of the one-dimensional Bose gas, aligning well with exact and numerical results across various interaction regimes.

Contribution

It introduces new approximate formulas for the dynamic structure factor that are valid over a wide parameter range and consistent with known exact results.

Findings

Approximate formulas match exact results in limiting cases.

Excellent agreement with algebraic Bethe ansatz numerical data.

Formulas encompass edge exponents, Luttinger liquid, and perturbative results.

Abstract

We discuss approximate formulas for the dynamic structure factor of the one-dimensional Bose gas in the Lieb-Liniger model that appear to be applicable over a wide range of the relevant parameters such as the interaction strength, frequency, and wavenumber. The suggested approximations are consistent with the exact results known in limiting cases. In particular, we encompass exact edge exponents as well as Luttinger liquid and perturbation theoretic results. We further discuss derived approximations for the static structure factor and the pair distribution function g(x). The approximate expressions show excellent agreement with numerical results based on the algebraic Bethe ansatz.