Strongly correlated fermions with nonlinear energy dispersion and spontaneous generation of anisotropic phases

Using the bosonization approach, we study fermionic systems with a nonlinear dispersion relation in dimension $d>~2.$ We explicitly show how the band curvature gives rise to interaction terms in the bosonic version of the model. Although these terms are perturbatively irrelevant in relation to the Landau Fermi-liquid fixed point, they become relevant perturbations when instabilities take place. Using a coherent-state path-integral technique, we built up the effective action that governs the dynamics of the Fermi-surface fluctuations. We consider the combined effect of fermionic interactions and band curvature on possible anisotropic phases triggered by negative Landau parameters (Pomeranchuck instabilities). In particular, we study in some detail the phase diagram for the isotropic/nematic/hexatic quantum phase transition.