  We construct an ionic lattice background in the framework of
Einstein-Maxwell-dilaton theory in four dimensional space time. The optical
conductivity of the dual field theory on the boundary is investigated. Due to
the lattice effects, we find the imaginary part of the conductivity is
manifestly suppressed in the zero frequency limit, while the DC conductivity
approaches a finite value such that the previous delta function reflecting the
translation symmetry is absent. Such a behavior can be exactly fit by the Drude
law at low frequency. Moreover, we find that the modulus of the optical
conductivity exhibits a power-law behavior at intermediate frequency regime.
Our results provides further support for the universality of such power-law
behavior recently disclosed in Einstein-Maxwell theory by Horowitz, Santos and
Tong.
