Auxiliary-field quantum Monte Carlo method for strongly paired fermions

We solve the zero-temperature unitary Fermi gas problem by incorporating a BCS importance function into the auxiliary-field quantum Monte Carlo method. We demonstrate that this method does not suffer from a sign problem and that it increases the efficiency of standard techniques by many orders of magnitude for strongly paired fermions. We calculate the ground-state energies exactly for unpolarized systems with up to 66 particles on lattices of up to ${27}^3$ sites, obtaining an accurate result for the universal parameter $\xi$. We also obtain results for interactions with different effective ranges and find that the energy is consistent with a universal linear dependence on the product of the Fermi momentum and the effective range. This method will have many applications in superfluid cold atom systems and in both electronic and nuclear structures where pairing is important.

Figure 1

The calculated ground-state energy shown as the value of $\xi$ vs the lattice size for various particle numbers and Hamiltonians.

Figure 2

The ground-state energy as a function of $k_F{r}_e$: comparison of DMC and AFQMC results. Dashed lines are DMC results, shifted down by 0.02 to enable comparison of the slopes.