##
Universal phase diagram of interacting
quantum liquids near the
unitarity limit

Predrag Nikolic**,
Harvard University**
__Abstract:__
We consider several models of particles with short-range attractive
interactions whose universal properties are controlled by an unstable
renormalization-group fixed point at zero density and temperature. The
fixed
point corresponds to the Feshbach resonance, and relevant perturbations
are the
detuning of the resonance, and parameters that control the particle
densities.
Some critical exponents are determined exactly, and scaling functions are
expressed as expansions about two and four spatial dimensions. The
existence of
a renormalization-group fixed point implies a universal phase diagram as a
function of density, temperature, population imbalance, and detuning. We
study
this phase diagram in the context of BEC-BCS crossover of s-wave paired
fermions. We develop a 1/N expansion, based upon models with Sp(2N)
symmetry,
which overcomes certain limitations of the expansions about two and four
dimensions. Using this approach we chart the phase diagram of uniform
ultra-cold fermions with population imbalance, as well as the
superfluid-insulator phase diagram of balanced fermions in a
three-dimensional
optical lattice.