Quantum critical fluctuations due to nested Fermi surface: The case of spinless fermions

A quantum critical point (QCP) can be obtained by tuning the critical temperature of a second-order phase transition to zero. A simple model of spinless fermions with nested Fermi surface leading to a charge density wave is considered. The QCP is obtained by tuning the nesting mismatch of the Fermi surface, which has the following consequences: (i) For the tuned QCP, the specific heat over T and the effective mass increase with the logarithm of the temperature as T is lowered. (ii) For the tuned QCP the linewidth of the quasi-particles is sublinear in T   and ωω. (iii) The specific heat and the linewidth display a crossover from non-Fermi liquid (∼T)(∼T) to Fermi liquid (∼T2)(∼T2) behavior with increasing nesting mismatch and decreasing temperature. (iv) For the tuned QCP, the dynamical charge susceptibility has a quasi-elastic peak with a linewidth proportional to T. (v) For non-critical Fermi vector mismatch the peak is inelastic. (vi) While the specific heat and the quasi-particle linewidth are only weakly dependent on the geometry of the nested Fermi surfaces, the momentum-dependent dynamical susceptibility is expected to be affected by the shape of the Fermi surface.