Truncated Calogero-Sutherland models

TL;DR

This paper introduces a tunable one-dimensional quantum many-body model with truncated inverse-square interactions, bridging the Calogero-Sutherland model and nearest-neighbor systems, and analyzes its ground state properties and collective excitations.

Contribution

It presents a novel truncated Calogero-Sutherland model with adjustable interaction range and explores its ground state wavefunction and collective modes.

Findings

Ground state wavefunction has a truncated Bijl-Jastrow form

Density profile and momentum distribution depend on interaction range

Model interpolates between known integrable systems

Abstract

A one-dimensional quantum many-body system consisting of particles confined in a harmonic potential and subject to finite-range two-body and three-body inverse-square interactions is introduced. The range of the interactions is set by truncation beyond a number of neighbors and can be tuned to interpolate between the Calogero-Sutherland model and a system with nearest and next-nearest neighbors interactions discussed by Jain and Khare. The model also includes the Tonks-Girardeau gas describing impenetrable bosons as well as a novel extension with truncated interactions. While the ground state wavefunction takes a truncated Bijl-Jastrow form, collective modes of the system are found in terms of multivariable symmetric polynomials. We numerically compute the density profile, one-body reduced density matrix, and momentum distribution of the ground state as a function of the range $r$ and the interaction strength.