Auxiliary Field quantum Monte Carlo for Strongly Paired Fermions

TL;DR

This paper introduces an improved auxiliary field quantum Monte Carlo method incorporating a BCS importance function, significantly enhancing efficiency for strongly paired fermions and accurately calculating properties of unpolarized Fermi gases at unitarity.

Contribution

The authors develop a new auxiliary field quantum Monte Carlo approach with a BCS importance function, eliminating the fermion sign problem and enabling precise calculations for strongly paired fermionic systems.

Findings

Achieved accurate ground-state energy for unpolarized Fermi gas at unitarity.

Demonstrated no fermion sign problem with the new method.

Results for different interactions converge to the same continuum limit.

Abstract

We demonstrate that the inclusion of a BCS importance function dramatically increases the efficiency of the auxiliary field method for strong pairing. We calculate the ground-state energy of an unpolarized fermi gas at unitarity with up to 66 particles and lattices of up to $27^3$ sites. The method has no fermion sign problem, and an accurate result is obtained for the universal parameter $\xi$. Several different forms of the kinetic energy adjusted to the unitary limit but with different effective ranges extrapolate to the same continuum limit within error bars. The finite effective range results for different interactions are consistent with a linear term proportional to the Fermi momentum times the effective range. The new method described herein will have many applications in superfluid cold atom systems and in both electronic and nuclear structures when pairing is important.