Extended study for unitary fermions on a lattice using the cumulant expansion technique

TL;DR

This paper introduces a cumulant expansion method for accurately computing ground state energies of large numbers of strongly interacting unitary fermions on lattices, overcoming distribution tail issues in correlator measurements.

Contribution

The authors develop and apply a cumulant expansion technique to determine energies of up to 66 unpolarized fermions on large lattices, improving accuracy and efficiency over standard methods.

Findings

Successfully measured energies for up to 66 fermions on large lattices.

Achieved good agreement with benchmark results for small fermion numbers.

Improved lattice action with Galilean invariance enhances predictive accuracy.

Abstract

A recently developed lattice method for large numbers of strongly interacting nonrelativistic fermions exhibits a heavy tail in the distributions of correlators for large Euclidean time {\tau} and large number of fermions N, which only allows the measurement of ground state energies for a limited number of fermions using standard techniques. In such cases, it is suggested that measuring the log of the correlator is more efficient, and a cumulant expansion of this quantity can be exactly related to the correlation function. The cumulant expansion technique allows us to determine the ground state energies of up to 66 unpolarized unitary fermions on lattices as large as 72$\times$14^3, and up to 70 unpolarized unitary fermions trapped in a harmonic potential on lattices as large as 72$\times$64^3. We have also improved our lattice action with a Galilean invariant form for the four-fermion interaction, which results in predictive volume scaling of the lowest energy of three fermions in a periodic box and in good agreement of our results for N \leq 6 trapped unitary fermions with those from other benchmark calculations.