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

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

2009-03-12

arxiv.org/abs/0903.2263v2

Phys. Rev. A 80, 013613 (2009)

Physics

Condensed Matter

Superconductivity

6 pages, 5 figures, Revtex4, final version

Scientific paper

10.1103/PhysRevA.80.013613

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.

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