We study a one-dimensional two-component Fermi gas in a harmonic trapping
potential using finite temperature lattice quantum Monte Carlo methods. We are
able to compute observables in the canonical ensemble via an efficient
projective approach. Results for density profiles, correlations, as well as
energy-related observables are presented for systems with up to 80 particles
and various temperatures. Our simulations reproduce known numerical results and
compare well against available experimental data close to the ground state,
while at higher temperature they are benchmarked against the exact solution of
the two particle system. This provides an indication that a standard lattice
discretization is sufficient to capture the physics of the trapped system. In
the special case of a spin-imbalanced gas, we find no sign problem in the
parameter ranges studied, allowing access without the need of specialized
methods. This includes simulations close to the ground state and at large
population imbalance, where we present results for density correlations,
indicating pairing at finite total momentum.Comment: 11 pages, 6 figure