Probing phase transitions of holographic entanglement entropy with fixed area states

TL;DR

This paper investigates corrections to holographic entanglement entropy near phase transitions, showing that these corrections smooth out the transition into a crossover, with explicit calculations supporting the conjectured diagonal approximation.

Contribution

It introduces a diagonal approximation for fixed-area states that predicts significant corrections near phase transitions, transforming sharp RT phase transitions into smooth crossovers.

Findings

Corrections near phase transitions are of order O(G^{-1/2}) and suppress the sharpness of RT phase transitions.

Explicit calculations for AdS3 and BTZ black hole boundary regions support the diagonal approximation.

The results align with predictions from chaotic many-body systems and previous quantum RT transition studies.

Abstract

Recent results suggest that new corrections to holographic entanglement entropy should arise near phase transitions of the associated Ryu-Takayanagi (RT) surface. We study such corrections by decomposing the bulk state into fixed-area states and conjecturing that a certain `diagonal approximation' will hold. In terms of the bulk Newton constant $G$, this yields a correction of order $O(G^{-1/2})$ near such transitions, which is in particular larger than generic corrections from the entanglement of bulk quantum fields. However, the correction becomes exponentially suppressed away from the transition. The net effect is to make the entanglement a smooth function of all parameters, turning the RT `phase transition' into a crossover already at this level of analysis. We illustrate this effect with explicit calculations (again assuming our diagonal approximation) for boundary regions given by a pair of disconnected intervals on the boundary of the AdS$_3$ vacuum and for a single interval on the boundary of the BTZ black hole. In a natural large-volume limit where our diagonal approximation clearly holds, this second example verifies that our results agree with general predictions made by Murthy and Srednicki in the context of chaotic many-body systems. As a further check on our conjectured diagonal approximation, we show that it also reproduces the $O(G^{-1/2})$ correction found Penington et al for an analogous quantum RT transition. Our explicit computations also illustrate the cutoff-dependence of fluctuations in RT-areas.