Dynamics of the Area Law of Entanglement Entropy

Abstract

We study the evolution of the universal area law of entanglement entropy when the Hamiltonian of the system undergoes a time dependent perturbation. In particular, we derive a general formula for the time dependent first order correction to the area law under the assumption that the field theory resides in a vacuum state when a small time-dependent perturbation of a relevant coupling constant is turned on. Using this formula, we carry out explicit calculations in free field theories deformed by a time dependent mass, whereas for a generic QFT we show that the time dependent first order correction is governed by the spectral function defining the two-point correlation function of the trace of the energy-momentum tensor. We also carry out holographic calculations based on the HRT proposal and find qualitative and, in certain cases, quantitative agreement with the field theory calculations.

26 pages, one figure. v2: published version

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• Holographic subregion complexity under thermal quench in Einstein-Maxwell-Axions theory with momentum relaxation
• Time dependence of reflected entropy in rational and holographic conformal field theories
• A Renyi Quantum Null Energy Condition: Proof for Free Field Theories
• The holographic dual of Rényi relative entropy
• Time Evolution after Double Trace Deformation
• Entanglement Entropy with a Time-dependent Hamiltonian