Fermionization in an expanding 1D gas of hard-core bosons

TL;DR

This paper demonstrates through exact numerical methods that a 1D gas of hard-core bosons undergoing free expansion exhibits fermionization in its momentum distribution, developing a Fermi edge, while maintaining a power-law decay in the density matrix.

Contribution

It provides a detailed analysis of the fermionization process in an expanding 1D hard-core boson gas, highlighting phenomena not observed in equilibrium.

Findings

Momentum distribution approaches that of noninteracting fermions with a Fermi edge.

Power-law decay of the one-particle density matrix persists during expansion.

Fermionization of the momentum distribution occurs dynamically, not in equilibrium.

Abstract

We show by means of an exact numerical approach that the momentum distribution of a free expanding gas of hard-core bosons on a one-dimensional lattice approaches to the one of noninteracting fermions, acquiring a Fermi edge. Yet there is a power-law decay of the one-particle density matrix $\rho_x\sim 1/\sqrt{x}$, as usual for hard-core bosons in the ground state, which accounts for a large occupation of the lowest natural orbitals for all expansion times. The fermionization of the momentum distribution function, which is not observed in equilibrium, is analyzed in detail.