Shell-Model Monte Carlo Simulations of BCS-BEC Crossover in Few-Fermion Systems

TL;DR

This paper uses shell-model Monte Carlo simulations to study the BCS-BEC crossover in few-fermion systems with zero-range interactions, providing ab initio results for energies across different regimes.

Contribution

It presents a novel application of shell-model Monte Carlo methods to finite fermion systems, addressing renormalization and convergence issues in the BCS-BEC crossover.

Findings

Accurate results on the BCS side of the crossover.

Less clear convergence at unitarity and BEC regimes.

Good agreement with existing two-body and literature results.

Abstract

We study a trapped system of fermions with a zero-range two-body interaction using the shell-model Monte Carlo method, providing {\em ab initio} results for the low particle number limit where mean-field theory is not applicable. We present results for the $N$-body energies as function of interaction strength, particle number, and temperature. The subtle question of renormalization in a finite model space is addressed and the convergence of our method and its applicability across the BCS-BEC crossover is discussed. Our findings indicate that very good quantitative results can be obtained on the BCS side, whereas at unitarity and in the BEC regime the convergence is less clear. Comparison to N=2 analytics at zero and finite temperature, and to other calculations in the literature for $N>2$ show very good agreement.