Holographic fermions on a charged Lifshitz background from Einstein-Dilaton-Maxwell model

Abstract

We study the properties of the fermionic response on a charged Lifshitz back- ground from Einstein-Dilaton-Maxwell model. First, we find that the Lifshitz dynamical exponent z plays the role smoothing out the quasi-particle-peak. Second, by numerical methods, we study the Fermi surface structure and the dispersion relation on this back- ground for a specific example of q = 0.5 and z = 1.02. One finds that the dispersion relation is non-linear, which indicates such a holographic system can be the candidates for holographic dual of generalized non-Fermi liquids. Third, by studying the dependence of the Fermi momentum kF on z, one observes that the Fermi momentum kF decreases with z increasing and when z > zcrit, the quasi-particle-like peak enters into the oscillatory region. Finally, by matching methods, we can also determined analytically the dispersion relation after the Fermi momentum is numerically worked out. One finds that the scaling exponent δ increases rapidly with z increasing, indicating that the degree of deviate from the Landau Fermi liquid becomes larger with z increasing. But the another scaling exponent β = 1, which is independent of z.