Holographic Approach to Entanglement Entropy in Disordered Systems

TL;DR

This paper uses holographic methods to analyze how entanglement entropy evolves in a disordered two-dimensional system, revealing universal behaviors and disorder effects during RG flows.

Contribution

It introduces a holographic framework to study entanglement entropy in disordered systems and uncovers universal power-law decay and disorder-induced correlations.

Findings

Disorder causes a sub-leading power-law term in entanglement entropy.

The power-law exponent is nearly universal, weakly depending on disorder strength.

Effective central charge decreases along the RG flow, consistent with the c-theorem.

Abstract

We investigate the entanglement entropy of a two-dimensional disordered system holographically. In particular, we study the evolution of the entanglement entropy along renormalization group flows for a conformal theory at the UV fixed point, that is perturbed by weak disorder into a Lifshitz theory at the IR fixed point. Through numerical fitting, we find that the disorder correlations leads to a sub-leading power-law term in the entanglement entropy that vanishes at the IR fixed point. Interestingly, the exponent that controls the power-law vanishing of the sub-leading term seems to be almost universal as it depends very weakly on the strength of the disorder. We show that our results can be put in the context of the c-theorem by defining an effective central charge that decreases along the RG flow. We also investigate disorder induced long-range correlations between the two subsystems by studying the holographic mutual information.