Lattice Monte Carlo calculations for unitary fermions in a harmonic trap

Abstract

We present a new lattice Monte Carlo approach developed for studying large numbers of strongly interacting nonrelativistic fermions and apply it to a dilute gas of unitary fermions confined to a harmonic trap. In place of importance sampling, our approach makes use of high statistics, an improved action, and recently proposed statistical techniques. We show how improvement of the lattice action can remove discretization and finite volume errors systematically. For N = 3 unitary fermions in a box, our errors in the energy scale as the inverse lattice volume, and we reproduce a previous high precision benchmark calculation to within our 0.3% uncertainty; as additional benchmarks we reproduce precision calculations of N = 3, ..., 6 unitary fermions in a harmonic trap to within our ∼ 1% uncertainty. We then use this action to determine the ground state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as 64 3 × 72. In contrast to variational calculations we find evidence for persistent deviations from the thermodynamic limit for the range of N considered.

Improved lattice operators for nonrelativistic fermions

“…Furthermore, comparing with the results of Ref. [4], it seems clear that one would need much larger lattices in the Galilean-invariant version to make Fig. 6 look like Fig.…”

Energy, contact, and density profiles of one-dimensional fermions in a harmonic trap via nonuniform-lattice Monte Carlo calculations

“…This is due to an "overlap problem" which affects calculations in all areas of physics (see, e.g., Ref. [22]). The Monte Carlo estimates of Ĥ were obtained by averaging over 10 4 de-correlated samples of the auxiliary field, which ensured a statistical uncertainty of order 1%.…”

Log-normal distribution for correlators in lattice QCD?

“…[1][2][3][4][5][6][7], that the second cumulant of log C(t), κ 2 , increases roughly linearly with time t.…”

“…[1][2][3][4][5][6][7] have shown that, for their data sets, noisy signals can be tamed by replacing the average correlator by a truncated cumulant sum,…”

“…It would be very interesting to look at distributions of And finally, can log-normality be used to do anything quantitative? So far, I have not been able to use it to improve mass determinations along the lines of [1][2][3][4][5][6][7].…”