Quasi-Long-Range Order in the Calogero-Sutherland Model

TL;DR

This paper investigates the ground-state properties of the one-dimensional Calogero-Sutherland model, demonstrating that it exhibits quasi-long-range positional order through numerical simulations and analytical arguments.

Contribution

It provides a detailed numerical and analytical analysis showing the presence of quasi-long-range order in the model's ground state, a novel insight into its phase behavior.

Findings

Quasi-long-range positional order exists for all parameter values.

The structure function and displacement correlations decay algebraically.

The ground state is a single normal phase with this order.

Abstract

The occurrence of quasi-long-range positional order in the ground-state of the one-dimensional repulsive Calogero-Sutherland model is studied. By mapping the exact ground-state into a one dimensional classical system of interacting particles at finite temperatures the structure function and the displacement correlation functions are calculated numerically using Monte Carlo simulation methods. These are found to exhibit quasi-long-range positional order for all values of the parameters. The exponent characterizing the algebraic decay of the displacement correlation functions with distance is estimated. It is argued that the ground-state of the repulsive Calogero-Sutherland model consists of a single normal phase with quasi-long-range positional order.