Abundance of Ground States with Positive Parity

TL;DR

This paper analyzes a random-matrix model for fermions with positive and negative parity states, showing that in the dilute limit, ground states of both parities occur with equal probability, highlighting finite-size effects.

Contribution

It provides an analytical and numerical study demonstrating that ground state parity probabilities are equal in the dilute limit, emphasizing finite-size effects.

Findings

Positive and negative parity ground states occur with equal probability in the dilute limit.

Differences in ground-state probabilities are due to Hilbert space dimension differences.

Finite-size effects dominate the parity distribution of ground states.

Abstract

We investigate analytically and numerically a random-matrix model for m fermions occupying l1 single-particle states with positive parity and l2 single-particle states with negative parity and interacting through random two-body forces that conserve parity. The single-particle states are completely degenerate and carry no further quantum numbers. We compare spectra of many-body states with positive and with negative parity. We show that in the dilute limit, ground states with positive and with negative parity occur with equal probability. Differences in the ground-state probabilities are, thus, a finite-size effect and are mainly due to different dimensions of the Hilbert spaces of either parity.