Entanglement Dynamics by (Non-)Unitary Local Operator Quenches in a 2D Holographic CFT

TL;DR

This paper studies how entanglement entropy and mutual information evolve in 2D holographic CFTs after local operator quenches, revealing differences between unitary and non-unitary time evolutions and their gravity duals involving black branes.

Contribution

It demonstrates the distinct effects of unitary and non-unitary local quenches on entanglement dynamics and explores their gravity dual descriptions with spacetime-dependent horizons.

Findings

Unitary evolution causes late-time logarithmic growth of entanglement entropy.

Non-unitary evolution leads to late-time constant entanglement entropy.

Gravity duals involve black branes with spacetime-dependent horizons.

Abstract

In this paper, we investigate the time evolution of entanglement entropy and mutual information for the spatially-infinite systems where we act with a primary operator on the vacuum state and then time-evolve it with the sequence of the Euclidean and Lorentzian time evolutions. Two-dimensional holographic conformal field theories describe the systems under consideration in this paper. The Euclidean time evolution is induced by the Rindler Hamiltonian and behaves as the regulator that tames the divergence induced by the local operator, while the Lorentzian one is induced by the uniform Hamiltonian. Under these time evolutions, we investigate the time ordering effect of the Rindler Euclidean and uniform Lorentzian time evolution operators. Consequently, we find the remarkable differences between those time evolutions are induced by whether those are unitary or non-unitary. Especially, we find that the unitary time evolution induces the late-time logarithmic growth of the entanglement entropy, while the non-unitary time evolution induces the late-time constant behavior. Furthermore, we investigate the dual gravity of the systems under consideration. Especially, we investigate the gravity duals of the systems with the insertion of the heavy primary operator and show that it is a black brane with a spacetime-dependent horizon.