Perturbative correction to the ground state properties of one-dimensional strongly interacting bosons in a harmonic trap

TL;DR

This paper computes the first-order correction to the ground state energy of strongly interacting bosons in a harmonic trap, revealing how interactions modify energy scaling for large particle numbers.

Contribution

It introduces a perturbative approach to quantify corrections beyond the Tonks-Girardeau limit for trapped bosons with contact interactions.

Findings

The $1/c$ correction to energy scales as $N^{5/2}$ for large N.

The unperturbed energy scales as $N^2$ in the Tonks-Girardeau limit.

A thermodynamic scaling limit reproduces known zero-temperature thermodynamics.

Abstract

We calculate the first-order perturbation correction to the ground state energy and chemical potential of a harmonically trapped boson gas with contact interactions about the infinite repulsion Tonks-Girardeau limit. With $c$ denoting the interaction strength, we find that for a large number of particles $N$ the $1/c$ correction to the ground state energy increases as $N^{5/2}$, in contrast to the unperturbed Tonks-Girardeau value that is proportional to $N^2$. We describe a thermodynamic scaling limit for the trapping frequency that yields an extensive ground state energy and reproduces the zero temperature thermodynamics obtained by a local density approximation.