  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. Our lattice action
is highly improved, with sources of discretization and finite volume errors
systematically removed; we are able to demonstrate the expected volume scaling
of energy levels of two and three untrapped fermions, and to reproduce the high
precision calculations published previously for the ground state energies for N
= 3 unitary fermions in a box (to within our 0.3% uncertainty), and for N = 3,
. . ., 6 unitary fermions in a harmonic trap (to within our ~ 1% uncertainty).
We 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 x 72; our approach avoids the use of importance sampling or calculation of
a fermion determinant and employs a novel statistical method for estimating
observables, allowing us to generate ensembles as large as 10^8 while requiring
only relatively modest computational resources.
