Applications of the Collective Field Theory for the Calogero-Sutherland Model

TL;DR

This paper applies collective field theory to the Calogero-Sutherland model to analyze low-energy properties, including ground state energy, sound mode dispersion, and soliton solutions, highlighting its applicability limits.

Contribution

It extends the application of collective field theory to detailed low-energy analyses of the Calogero-Sutherland model, including new insights into soliton solutions and correlation functions.

Findings

Ground state energy computed up to two leading orders in particle number.

Dispersion relation of sound modes matches low-temperature specific heat behavior.

Two-point correlation function accurately describes nonoscillatory asymptotic behavior.

Abstract

We use the collective field theory known for the Calogero-Sutherland model to study a variety of low-energy properties. These include the ground state energy in a confining potential upto the two leading orders in the particle number, the dispersion relation of sound modes with a comparison to the two leading terms in the low temperature specific heat, large amplitude waves, and single soliton solutions. The two-point correlation function derived from the dispersion relation of the sound mode only gives its nonoscillatory asymptotic behavior correctly, demonstrating that the theory is applicable only for the low-energy and long wavelength excitations of the system.