  Strongly correlated Fermi systems with pairing interactions become superfluid
below a critical temperature $T_c$. The extent to which such pairing
correlations alter the behavior of the liquid at temperatures $T > T_c$ is a
subtle issue that remains an area of debate, in particular regarding the
appearance of the so-called pseudogap in the BCS-BEC crossover of unpolarized
spin-$1/2$ nonrelativistic matter. To shed light on this, we extract several
quantities of crucial importance at and around the unitary limit, namely: the
odd-even staggering of the total energy, the spin susceptibility, the pairing
correlation function, the condensate fraction, and the critical temperature
$T_c$, using a non-perturbative, constrained-ensemble quantum Monte Carlo
algorithm.
