Edge exponent in the dynamic spin structure factor of the Yang-Gaudin model

TL;DR

This paper investigates the dynamic spin structure factor of spin-1/2 bosons with arbitrary interactions, revealing a power-law singularity at the magnon energy threshold and calculating its exponent exactly.

Contribution

It provides an exact calculation of the power-law exponent for the singularity in the dynamic spin structure factor of the Yang-Gaudin model using Bethe Ansatz and effective field theory.

Findings

Power-law singularity at the magnon threshold frequency.

Exact determination of the singularity exponent.

Applicability to arbitrary interaction strengths.

Abstract

The dynamic spin structure factor $\mathcal{S}(k,\omega)$ of a system of spin-1/2 bosons is investigated at arbitrary strength of interparticle repulsion. As a function of $\omega$ it is shown to exhibit a power-law singularity at the threshold frequency defined by the energy of a magnon at given $k.$ The power-law exponent is found exactly using a combination of the Bethe Ansatz solution and an effective field theory approach.