Dynamical entanglement entropy with angular momentum and U(1) charge

TL;DR

This paper studies the time evolution of entanglement entropy in a 1+1D CFT with angular momentum and U(1) charge, showing saturation to grand canonical entropy and connecting holographic and field theory results.

Contribution

It provides a detailed analysis of entanglement entropy dynamics in charged, rotating systems and resolves discrepancies between holographic and CFT calculations.

Findings

EE saturates to grand canonical entropy after long times

Holographic and CFT EE results are reconciled through charge-dependent shifts

EE obeys the first law of thermodynamics for small intervals

Abstract

We consider time-dependent entanglement entropy (EE) for a 1+1 dimensional CFT in the presence of angular momentum and U(1) charge. The EE saturates, irrespective of the initial state, to the grand canonical entropy after a time large compared with the length of the entangling interval. We reproduce the CFT results from an AdS dual consisting of a spinning BTZ black hole and a flat U(1) connection. The apparent discrepancy that the holographic EE does not a priori depend on the U(1) charge while the CFT EE does, is resolved by the charge-dependent shift between the bulk and boundary stress tensors. We show that for small entangling intervals, the entanglement entropy obeys the first law of thermodynamics, as conjectured recently. The saturation of the EE in the field theory is shown to follow from a version of quantum ergodicity; the derivation indicates that it should hold for conformal as well as massive theories in any number of dimensions.