  Chang and Bertsch [Phys. Rev. A 76, 021603(R) (2007)] proposed a simple
formula for the ground state energy of a unitary Fermi gas in a harmonic trap,
based on their Green's function Monte Carlo simulations of up to 22 fermions,
combined with general assumptions about the universal thermodynamic behavior of
the unitary Fermi gas. In this work, we perform the ab initio simulations of
the ground state energy of up to one hundred fermions using the fictitious
identical particle method to overcome the Fermion sign problem, and we find
that the formula proposed by Chang and Bertsch remains highly accurate. Since
the number of fermions we simulate is much larger than that simulated by Chang
and Bertsch when they proposed the formula, our work provides strong evidence
for the universal validity of the formula. Our work demonstrates that
fictitious identical particles provide a valuable tool for the ab initio
simulations of ultracold Fermi gases.
