Further Evidence for Lattice-Induced Scaling

TL;DR

This paper provides additional evidence that a background lattice in holographic models induces an intermediate scaling regime in transport properties, matching experimental observations in cuprates, and extends the findings to different spacetime dimensions and lattice types.

Contribution

It demonstrates the robustness of the lattice-induced scaling regime across various holographic models and lattice configurations, including thermoelectric conductivity and higher-dimensional spacetimes.

Findings

Optical conductivity exhibits a power-law dependence $\sigma \sim \omega^{-2/3}$ in the mid-infrared regime.

Similar scaling behavior is observed in thermoelectric conductivity.

Scaling results are consistent across different spacetime dimensions and lattice types.

Abstract

We continue our study of holographic transport in the presence of a background lattice. We recently found evidence that the presence of a lattice induces a new intermediate scaling regime in asymptotically $AdS_4$ spacetimes. This manifests itself in the optical conductivity which exhibits a robust power-law dependence on frequency, $\sigma \sim \omega^{-2/3}$, in a "mid-infrared" regime, a result which is in striking agreement with experiments on the cuprates. Here we provide further evidence for the existence of this intermediate scaling regime. We demonstrate similar scaling in the thermoelectric conductivity, find analogous scalings in asymptotically $AdS_5$ spacetimes, and show that we get the same results with an ionic lattice.