A Simple Holographic Model of a Charged Lattice

TL;DR

This paper employs holography to analyze conductivity in an inhomogeneous charged scalar background, revealing spectral weight transfer phenomena and Drude-like behavior through analytical and numerical methods.

Contribution

It introduces a holographic model with a striped scalar deformation to study conductivity, combining analytical and numerical techniques in an inhomogeneous setting.

Findings

Analytical conductivity at zero temperature shows a small amplitude expansion.

Numerical results at finite temperature demonstrate a Drude-like peak.

Spectral weight transfer explains the negative weight delta function.

Abstract

We use holography to compute the conductivity in an inhomogeneous charged scalar background. We work in the probe limit of the four-dimensional Einstein-Maxwell theory coupled to a charged scalar. The background has zero charge density and is constructed by turning on a scalar source deformation with a striped profile. We solve for fluctuations by making use of a Fourier series expansion. This approach turns out to be useful for understanding which couplings become important in our inhomogeneous background. At zero temperature, the conductivity is computed analytically in a small amplitude expansion. At finite temperature, it is computed numerically by truncating the Fourier series to a relevant set of modes. In the real part of the conductivity along the direction of the stripe, we find a Drude-like peak and a delta function with a negative weight. These features are understood from the point of view of spectral weight transfer.