  We calculate the entanglement entropy of strongly correlated low-dimensional
fermions in metallic, superfluid and antiferromagnetic insulating phases. The
entanglement entropy reflects the degrees of freedom available in each phase
for storing and processing information, but is found not to be a state function
in the thermodynamic sense. The role of critical points, smooth crossovers and
Hilbert space restrictions in shaping the dependence of the entanglement
entropy on the system parameters is illustrated for metallic, insulating and
superfluid systems. The dependence of the spin susceptibility on entanglement
in antiferromagnetic insulators is obtained quantitatively. The opening of spin
gaps in antiferromagnetic insulators is associated with enhanced entanglement
near quantum critical points.
