Approximate expression for the dynamic structure factor in the Lieb-Liniger model

TL;DR

This paper develops an approximate formula for the dynamic structure factor of the 1D Bose gas, integrating recent theoretical and numerical insights to provide a practical expression consistent with known limits.

Contribution

It introduces an interpolation formula for the DSF of the 1D Bose gas that combines recent power-law behavior results with strong-coupling expansions.

Findings

The formula matches low-energy Luttinger liquid exponents.

It agrees well with recent numerical data.

It captures power-law behavior along collective mode dispersion.

Abstract

Recently, Imambekov and Glazman [Phys. Rev. Lett. 100, 206805 (2008)] showed that the dynamic structure factor (DSF) of the 1D Bose gas demonstrates power-law behaviour along the limiting dispersion curve of the collective modes and calculated the corresponding exponents exactly. Combining these recent results with a previously obtained strong-coupling expansion we present an interpolation formula for the DSF of the 1D Bose gas. The obtained expression is further consistent with exact low energy exponents from Luttinger liquid theory and shows nice agreement with recent numerical results.