Dynamic correlations in Calogero-Sutherland model

TL;DR

This paper develops a stochastic method combining sum rules and Monte Carlo techniques to analyze dynamic correlations in the Calogero-Sutherland model, covering various interaction regimes and connecting to broader physical systems.

Contribution

It introduces a novel stochastic approach to compute the dynamic structure factor in the Calogero-Sutherland model, extending analysis beyond traditional regimes.

Findings

Exact description of excitations across interaction regimes

Emergence of Bogoliubov spectrum in weak interactions

Brillouin zone structure in strong interactions

Abstract

The Calogero-Sutherland model represents a paradigmatic example of an integrable quantum system with applications ranging from cold atoms to random matrix theory. Combining sum rules with the Monte Carlo technique, we introduce a stochastic method that allows one to compute the dynamic structure factor and obtain an exact description of excitations beyond the conventional Luttinger liquid regime. We explore a broad range of interaction regimes, including weak interactions, where a Bogoliubov-type spectrum emerges, the Tonks-Girardeau regime, where excitations resemble those of an ideal Fermi gas, and strong interactions, where umklapp scattering leads to a Brillouin zone structure, typical of a crystal. Additionally, we discuss the connection between the hydrodynamic description of one-dimensional quantum gases, liquids, and solids with the Calogero-Sutherland wave function. The model's universality extends beyond atoms in waveguides, with implications for disordered systems and random matrix theory.