Dynamic structure factor of the Calogero-Sutherland model

TL;DR

This paper calculates the dynamic structure factor of the Calogero-Sutherland model, revealing finite frequency intervals with power-law singularities at the edges, influenced solely by interaction strength.

Contribution

It provides an exact evaluation of the dynamic structure factor for the Calogero-Sutherland model, highlighting the nature of singularities and their dependence on interaction parameters.

Findings

Finite frequency interval where $S(q,\omega)$ is non-zero

Power-law singularities at the interval borders

Singularity exponents depend only on interaction strength

Abstract

We evaluate the dynamic structure factor $S(q,\omega)$ of a one-dimensional quantum Hamiltonian with the inverse-square interaction (Calogero-Sutherland model). For a fixed small $q$, the structure factor differs from zero in a finite interval of frequencies of the width $\delta\omega\propto q^2/m$. At the borders of this interval $S(q,\omega)$ exhibits power-law singularities with exponents depending only on the interaction strength. The singularities are similar in origin to the well-known Fermi-edge singularity in the X-ray absorption spectra of metals.