Number-parity effect for confined fermions in one dimension

TL;DR

This paper discovers a parity-dependent effect in the spectrum of the one-particle reduced density matrix for a system of one-dimensional spin-polarized fermions with harmonic interactions, highlighting a unique quantum phenomenon absent in bosonic systems.

Contribution

It reveals a novel number-parity effect in the spectral properties of confined fermions, emphasizing the role of exchange statistics and interaction strength.

Findings

Parity affects the spectrum of the reduced density matrix for strong interactions.

Density and correlation functions do not show parity dependence for strong attractive interactions.

The effect is absent in bosonic systems, indicating a fermionic origin.

Abstract

For $N$ spin-polarized fermions with harmonic pair interactions in a $1$-dimensional trap an odd-even effect is found. The spectrum of the $1$-particle reduced density matrix of the system's ground state differs qualitatively for $N$ odd and $N$ even. This effect does only occur for strong attractive and repulsive interactions. Since it does not exists for bosons, it must originate from the repulsive nature implied by the fermionic exchange statistics. In contrast to the spectrum, the $1$-particle density and correlation function for strong attractive interactions do not show any sensitivity on the number parity. This also suggests that reduced-density-matrix-functional theory has a more subtle $N$-dependency than density functional theory.