On the Spread of Entanglement at Finite Cutoff

TL;DR

This paper investigates how entanglement propagates in finite-cutoff holographic theories with various cosmological constants, analyzing phase transitions and entanglement dynamics using the entanglement tsunami model.

Contribution

It provides a comprehensive analysis of entanglement spread and phase transitions in finite-cutoff holographic theories with different cosmological constants, extending previous studies.

Findings

Identifies a phase transition at equal cycle lengths in all three cases.

Analyzes entanglement entropy evolution in thermofield double states.

Proposes an entanglement tsunami interpretation for entropy dynamics.

Abstract

We study how entanglement spreads in the boundary duals of finite-cutoff three-dimensional theories with positive, negative and zero cosmological constant, the $T \bar{T} + \Lambda_{2}$ two-dimensional theories. We first study the Hawking-Page transition in all three cases, and find that there is a transition in all three scenarios at the temperature where the lengths of the two cycles of the torus are the same. We then study the entanglement entropy in the thermofield double states above the Hawking-Page transition, of regions symmetrically placed on the two boundaries. We consider the case where the region is one interval on each side, and the case where it is two intervals on each side. We give an entanglement tsunami interpretation of the time-evolution of the entanglement entropies.