One-dimensional fermionic gases with attractive p-wave interaction in a hard-wall trap

TL;DR

This paper studies the ground state properties of one-dimensional fermionic gases with attractive p-wave interactions in a hard-wall trap, deriving exact wave functions and analyzing density and momentum distributions.

Contribution

It provides an exact solution for the ground state of 1D fermionic gases with attractive p-wave interactions using Bethe ansatz, revealing detailed many-body properties.

Findings

Shell structure disappears with increasing interaction strength.

In the fermionic Tonks-Girardeau limit, density resembles an ideal Bose gas.

One-body density matrix and momentum distribution differ significantly from bosonic cases.

Abstract

We investigate the ground state of the one-dimensional fermionic system enclosed in a hard-wall trap with attractive contact p-wave interactions. Based on the Bethe ansatz method, the explicit wave function is derived by numerically solving the Bethe ansatz equations for the full physical regimes ($-\infty \leq c_F\leq 0$). With the exact wave function some quantities which are important in many-body physics are obtained, including the one-body density matrix and the momentum distribution of the ground state for finite system. It is shown that the shell structure of the density profiles disappears with the increase of the interaction and in the fermionic Tonks-Girardeau (FTG) limit the density distribution shows the same behavior as that of an ideal Bose gas. However the one-body density matrix and the momentum distribution exhibit completely different structures compared with their bosonic counterparts.