Bosonic models with Fermi-liquid kinematics: realizations and properties

We consider models of interacting bosons in which the single-particle kinetic energy achieves its minimum on a surface in momentum space. The kinematics of such models resembles that resulting from Pauli blocking in Fermi liquids; therefore, Shankar's renormalization-group treatment of Fermi liquids [1] can be adapted to investigate phase transitions in these bosonic systems. We explore possible experimental realizations of such models in cold atomic gases: e.g., via spin-orbit coupling [2], multimode-cavity-mediated interactions [3], and Cooper pairing of Fermi gases in spin-dependent lattices. We address the phase structure and critical behavior of the resulting models within the framework of Ref. [1], focusing in particular on Bose-Einstein condensation and on quantum versions of the Brazovskii transition from a superfluid to a supersolid [3]. \\[4pt] [1] R. Shankar, Rev. Mod. Phys. 66, 129-192 (1994) \\[0pt] [2] C. Wang et al., Phys. Rev. Lett. 105, 160403 (2010) \\[0pt] [3] S. Gopalakrishnan, B.L. Lev, and P.M. Goldbart, Nat. Phys. 5, 845-850 (2009)