We study the optical conductivity in a (2 + 1)-dimensional non-relativistic field theory holographically dual to a (3 + 1)-dimensional charged Lifshitz black brane within the Einstein-Maxwell-dilaton theory. Surprisingly, we find that the optical AC conductivity satisfies the nontrivial (non-)power law scaling in the high frequency regime rather than approaching to a constant when the dynamical critical exponent z> 1, which is qualitatively similar to those in various disordered solids in condensed matter systems. Besides, this (non-)power law scaling behavior shows some universality, which is robust against the temperatures. We argue that the peculiar scaling behavior of AC conductivity may stem from the couplings of the dilaton field with the gauge fields and also the logarithmic behavior near the boundary in the Lifshitz spacetime.
Sun, J. R., Wu, S. Y., & Zhang, H. Q. (2014). Mimic the optical conductivity in disordered solids via gauge/gravity duality. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 729, 177–184. https://doi.org/10.1016/j.physletb.2014.01.005