Ground-state properties of hard core bosons in one-dimensional harmonic traps

TL;DR

This paper numerically investigates the ground-state properties of hard core bosons in a one-dimensional harmonic trap, revealing the absence of Bose-Einstein condensation and scaling behaviors of key properties.

Contribution

It provides a detailed numerical analysis of the one-particle density matrix for large systems of hard core bosons, highlighting their non-condensed nature and scaling relations.

Findings

Ground state is not Bose-Einstein condensed.

Density matrix near diagonal resembles that of noninteracting fermions.

Key properties scale as powers of particle number with related exponents.

Abstract

The one-particle density matrices for hard core bosons in a one-dimensional harmonic trap are computed numerically for systems with up to 160 bosons. Diagonalization of the density matrix shows that the many-body ground state is not Bose-Einstein condensed. The ground state occupation, the amplitude of the lowest natural orbital, and the zero momentum peak height scale as powers of the particle number, and the corresponding exponents are related to each other. Close to its diagonal, the density matrix for hard core bosons is similar to the one of noninteracting fermions.