Thermodynamics of balanced and slightly spin-imbalanced Fermi gases at unitarity

In this article we present a Monte Carlo calculation of the critical temperature and other thermodynamic quantities for the unitary Fermi gas with a population imbalance (unequal number of fermions in the two spin components). We describe an improved worm-type algorithm that is less prone to autocorrelations than the previously available methods and show how this algorithm can be applied to simulate the unitary Fermi gas in presence of a small imbalance. Our data indicate that the critical temperature remains almost constant for small imbalances h = Δμ/ε _F &z.lap; 0.2. We obtain the continuum result T _c = 0.171(5)ε _F in units of Fermi energy and derive a lower bound on the deviation of the critical temperature from the balanced limit, T _c(h) - T _c(0) > -0.5ε _F h ². Using an additional assumption a tighter lower bound can be obtained. We also calculate the energy per particle and the chemical potential in the balanced and imbalanced cases.