Momentum distribution for a one-dimensional trapped gas of hard-core bosons

TL;DR

This paper develops an algorithm to compute the momentum distribution of a one-dimensional trapped hard-core boson gas using the exact ground state wave function, providing accurate results for small systems and comparing to analytic approximations.

Contribution

It introduces a new algorithm for calculating the momentum distribution from the exact ground state of a trapped 1D hard-core boson system, enabling precise numerical analysis.

Findings

Numerical results for up to 8 particles show detailed momentum distributions.

Comparison indicates the accuracy of the analytic approximation.

The method enhances understanding of quantum correlations in 1D bosonic systems.

Abstract

Using the exact $N$-particle ground state wave function for a one-dimensional gas of hard-core bosons in a harmonic trap we develop an algorithm to compute the reduced single-particle density matrix and corresponding momentum distribution. Accurate numerical results are presented for up to N=8 particles, and the momentum distributions are compared to a recent analytic approximation.