Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas

TL;DR

This paper precisely calculates the edge singularity exponents in the dynamic correlation functions of a 1D Bose gas, revealing their dependence on interaction strength and showing deviations from Luttinger liquid theory predictions.

Contribution

It provides exact exponents for edge singularities in the Lieb-Liniger model, connecting Bethe ansatz solutions to dynamic correlation function analysis.

Findings

Exponents vary significantly with interaction strength and momentum.

Luttinger liquid theory fails near the spectral edges.

Exact Bethe ansatz methods yield precise singularity exponents.

Abstract

The spectral function and dynamic structure factor of bosons interacting by contact repulsion and confined to one dimension exhibit power-law singularities along the dispersion curves of the collective modes. We find the corresponding exponents exactly, by relating them to the known Bethe ansatz solution of the Lieb-Liniger model. The found exponents vary considerably with the interaction strength and momentum. Remarkably, the Luttinger liquid theory predictions for the exponents fail even at low energies, once the immediate vicinities of the edges are considered.