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

A bstract 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...

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Bibliographic Details
Published in:The journal of high energy physics 2013-11, Vol.2013 (11), p.1-25, Article 52
Main Authors: Caputa, Paweł, Mandal, Gautam, Sinha, Ritam
Format: Article
Language:English
Subjects:
Angular momentum
Boundaries
Charge
Classical and Quantum Gravitation
Derivation
Elementary Particles
Entanglement
Entropy
High energy physics
Intervals
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Relativity Theory
Saturation
String Theory
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Summary:A bstract 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP11(2013)052