Enhanced corrections near holographic entanglement transitions: a chaotic case study

TL;DR

This paper investigates enhanced corrections to holographic entanglement entropy near phase transitions, using a chaotic eigenstate model and summing over bulk saddle points to understand the phenomenon.

Contribution

It introduces a method to compute enhanced entanglement corrections holographically by summing over all bulk saddle points, including symmetry-breaking solutions.

Findings

Enhanced corrections appear near holographic entanglement transitions.

Sum over saddle points can be expressed via an effective action for cosmic branes.

Results organize in fixed-area states, clarifying the correction structure.

Abstract

Recent work found an enhanced correction to the entanglement entropy of a subsystem in a chaotic energy eigenstate. The enhanced correction appears near a phase transition in the entanglement entropy that happens when the subsystem size is half of the entire system size. Here we study the appearance of such enhanced corrections holographically. We show explicitly how to find these corrections in the example of chaotic eigenstates by summing over contributions of all bulk saddle point solutions, including those that break the replica symmetry. With the help of an emergent rotational symmetry, the sum over all saddle points is written in terms of an effective action for cosmic branes. The resulting Renyi and entanglement entropies are then naturally organized in a basis of fixed-area states and can be evaluated directly, showing an enhanced correction near holographic entanglement transitions. We comment on several intriguing features of our tractable example and discuss the implications for finding a convincing derivation of the enhanced corrections in other, more general holographic examples.