Holographic entanglement negativity and replica symmetry breaking

TL;DR

This paper explores holographic entanglement negativity and Renyi negativities, revealing how replica symmetry breaking solutions in gravity duals influence these measures and connecting them with random tensor network models.

Contribution

It introduces a detailed analysis of Renyi negativities in holography, including the role of replica symmetry breaking, and establishes their equivalence with random tensor network results in fixed-area states.

Findings

Renyi negativities often dominated by replica symmetry breaking bulk solutions

Derived general expressions for Renyi negativities in holographic theories

Results in fixed-area states match random tensor network calculations

Abstract

Since the work of Ryu and Takayanagi, deep connections between quantum entanglement and spacetime geometry have been revealed. The negative eigenvalues of the partial transpose of a bipartite density operator is a useful diagnostic of entanglement. In this paper, we discuss the properties of the associated entanglement negativity and its R\'enyi generalizations in holographic duality. We first review the definition of the R\'enyi negativities, which contain the familiar logarithmic negativity as a special case. We then study these quantities in the random tensor network model and rigorously derive their large bond dimension asymptotics. Finally, we study entanglement negativity in holographic theories with a gravity dual, where we find that R\'enyi negativities are often dominated by bulk solutions that break the replica symmetry. From these replica symmetry breaking solutions, we derive general expressions for R\'enyi negativities and their special limits including the logarithmic negativity. In fixed-area states, these general expressions simplify dramatically and agree precisely with our results in the random tensor network model. This provides a concrete setting for further studying the implications of replica symmetry breaking in holography.