Entanglement Entropy with a Time-dependent Hamiltonian

TL;DR

This paper investigates how entanglement entropy evolves in a 2D conformal field theory with a time-dependent Hamiltonian, revealing universal structures and mechanisms of entanglement propagation through higher-order corrections and entanglement diagrams.

Contribution

It introduces a universal framework for entanglement propagation in time-dependent systems and develops entanglement diagrams to analyze higher-order corrections in holographic and CFT contexts.

Findings

First-order metric perturbation matches between CFT and AdS$_3$.

Interactions entangle initially unentangled excitations.

Tools for simplifying loop entanglement diagram computations.

Abstract

The time evolution of entanglement tracks how information propagates in interacting quantum systems. We study entanglement entropy in CFT$_2$ with a time-dependent Hamiltonian. We perturb by operators with time-dependent source functions and use the replica trick to calculate higher order corrections to entanglement entropy. At first order, we compute the correction due to a metric perturbation in AdS$_3$/CFT$_2$ and find agreement on both sides of the duality. Past first order, we find evidence of a universal structure of entanglement propagation to all orders. The central feature is that interactions entangle unentangled excitations. Entanglement propagates according to "entanglement diagrams," proposed structures that are motivated by accessory spacetime diagrams for real-time perturbation theory. To illustrate the mechanisms involved, we compute higher-order corrections to free fermion entanglement entropy. We identify an unentangled operator, one which does not change the entanglement entropy to any order. Then, we introduce an interaction and find it changes entanglement entropy by entangling the unentangled excitations. The entanglement propagates in line with our conjecture. We compute several entanglement diagrams. We provide tools to simplify the computation of loop entanglement diagrams, which probe UV effects in entanglement propagation in CFT and holography.