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.
Highlights
Always UV divergent [11, 12], whereas the structure of these divergences is state independent, see e.g., [13]
We study the evolution of the universal area law of entanglement entropy when the Hamiltonian of the system undergoes a time dependent perturbation
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 energymomentum tensor
Summary
We consider a CFT in d spacetime dimensions on the boundary, dual to Einstein gravity in the d + 1-dimensional bulk. Through the Einstein-scalar field equations, this will change the bulk metric and affect the calculation of the HRT surface and its area. The UV divergences in the entanglement entropy arise from the divergences of the area functional of the HRT surface, ΣB, near the asymptotic boundary (z = 0). To compute these divergences, we need to find the area functional, or the induced metric on ΣB, near z = 0. In [13], all the powers of z that arise in the asymptotic solution have been identified Using their result, we make the following ansatz for the metric and the scalar field: h(z, t) = 1 +.
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