Shell-Model Monte Carlo Simulations of Pairing in Few-Fermion Systems

TL;DR

This paper uses Shell-Model Monte Carlo simulations to analyze pairing phenomena in few-fermion systems with attractive interactions, revealing shell effects and phase transition signatures at finite temperature.

Contribution

It provides ab initio results for small fermion systems where mean-field approaches fail, highlighting shell effects and temperature-driven phase transitions.

Findings

Large odd-even effects observed

Shell structure signatures identified

Phase transition indicated by effects disappearance

Abstract

We study a trapped system of fermions with an attractive zero-range two-body interaction using the Shell-Model Monte Carlo method. The method provides {\em ab initio} results in the low $N$ limit where mean-field theory is not applicable. The energy and pairing properties are presented as functions of interaction strength, particle number, and temperature. In the interesting region where typical matrix elements of the two-body interaction are comparable to the level spacing of the trap we find large odd-even effects and signatures of shell structure. As a function of temperature, we observe the disappearance of these effects as in a phase transition.