Holographic fermions in charged Lifshitz theory

TL;DR

This paper explores the behavior of holographic fermions in charged Lifshitz black holes at finite temperature, revealing linear dispersion relations and the effects of dynamical exponent variations on Green function properties.

Contribution

It provides new insights into the properties of holographic fermions in charged Lifshitz backgrounds with different dynamical exponents, including dispersion relations and Green function scaling behaviors.

Findings

Linear dispersion relation observed at z=2

Green function scaling behavior analyzed

ImG becomes smoother as z increases

Abstract

We investigate the properties of holographic fermions in charged Lifshitz black holes at finite temperature through the AdS/CFT correspondence. In the charged Lifshitz background with the dynamical exponent $z=2$, we find that the dispersion relation is linear. The scaling behavior of the imaginal part of the Green function relative to $k_{\perp}=k-k_F$ is also discussed. We find, although the system has linear dispersion relation and quadratic quasi-particle width, it does not satisfy Luttinger's theorem. We also find that the variation of the scaling parameters $\alpha$ and $\beta$ is small as the charge $q$ varies. Furthermore, we also discuss the effect of the dynamical exponent $z$ by considering the cases $z=4$ and $z=6$ and show that $ImG_{ii}$ become smooth when the dynamical exponent $z$ increases.