Off-diagonal correlations of the Calogero-Sutherland model

TL;DR

This paper provides analytical and numerical insights into the correlation functions of the Calogero-Sutherland model across all interaction strengths, revealing detailed physical regimes and phase behaviors.

Contribution

It introduces new analytical expressions for the one-body density matrix and confirms them with Monte Carlo simulations, covering the entire interaction parameter range.

Findings

Analytical expressions for long-distance asymptotics of the one-body density matrix.

Numerical Monte Carlo results match analytical predictions.

Identification of various physical regimes including quasi-condensation and quasi-crystallization.

Abstract

We study correlation functions of the Calogero-Sutherland model in the whole range of the interaction parameter. Using the replica method we obtain analytical expressions for the long-distance asymptotics of the one-body density matrix in addition to the previously derived asymptotics of the pair-distribution function [D.M. Gangardt and A. Kamenev, Nucl. Phys. B, 610, 578 (2001)]. The leading analytic and non-analytic terms in the short-distance expansion of the one-body density matrix are discussed. Exact numerical results for these correlation functions are obtained using Monte Carlo techniques for all distances. The momentum distribution and static structure factor are calculated. The potential and kinetic energies are obtained using the Hellmann-Feynman theorem. Perfect agreement is found between the analytical expressions and numerical data. These results allow for the description of physical regimes of the Calogero-Sutherland model. The zero temperature phase diagram is found to be of a crossover type and includes quasi-condensation, quasi-crystallization and quasi-supersolid regimes.