The instability of $AdS$ black holes with lattices

TL;DR

This paper studies the stability of AdS black holes with lattice structures, revealing how different lattice types influence their instability and potential to model charge density waves in holography.

Contribution

It demonstrates that homogeneous axion fields suppress instability, while Q-lattices reduce the unstable region near phase transitions, offering new insights into holographic phase behavior.

Findings

Homogeneous axion fields suppress AdS-RN black hole instability.

Q-lattices minimize unstable regions near metal/insulator transition.

Instability behavior parallels holographic entanglement entropy during phase transitions.

Abstract

The Anti-de Sitter (AdS) black hole with lattice structure plays an essential role in the study of the optical conductivity in holographic approach. We investigate the instability of this sort of black holes which may lead to the holographic description of charge density waves. In the presence of homogeneous axion fields, we show that the instability of AdS-Reissner-Nordstr\"om(AdS-RN) black hole is always suppressed. However, in the presence of Q-lattices, we find that the unstable region becomes the smallest in the vicinity of the critical region for metal/insulator phase transition. This novel phenomenon is reminiscent of the behavior of the holographic entanglement entropy during quantum phase transition.