Off-diagonal Ground State Properties of a 1D Gas of Fermi Hard Rods

TL;DR

This paper uses variational Monte Carlo to accurately compute ground state properties of a 1D Fermi gas of hard rods, revealing how fermionic and bosonic systems converge at high densities.

Contribution

It provides the first exact Monte Carlo calculations of the one-body density matrix and momentum distribution for 1D Fermi hard rods, comparing them with bosonic counterparts.

Findings

Fermionic and bosonic density matrices become similar at high densities.

Momentum distributions of fermions and bosons merge at high densities.

Non-analytical contributions diminish as density increases.

Abstract

A variational Monte Carlo calculation of the one-body density matrix and momentum distribution of a system of Fermi hard rods (HR) is presented and compared with the same quantities for its bosonic counterpart. The calculation is exact within statistical errors since we sample the exact ground state wave function, whose analytical expression is known. The numerical results are in good agreement with known asymptotic expansions valid for Luttinger liquids. We find that the difference between the absolute value of the bosonic and fermionic density matrices becomes marginally small as the density increases. In this same regime, the corresponding momentum distributions merge into a common profile that is independent of the statistics. Non-analytical contributions to the one--body density matrix are also discussed and found to be less relevant with increasing density.