First law and quantum correction for holographic entanglement contour
Han M, Wen Q (2021)
Publication Type: Journal article, Review article
Publication year: 2021
Journal
Book Volume: 11
Article Number: 058
Journal Issue: 3
DOI: 10.21468/SCIPOSTPHYS.11.3.058
Abstract
Entanglement entropy satisfies a first law-like relation, which equates the first order perturbation of the entanglement entropy for the region A to the first order perturbation of the expectation value of the modular Hamiltonian, δSA = δ〈KA〉. We propose that this relation has a finer version which states that, the first order perturbation of the entanglement contour equals to the first order perturbation of the contour of the modular Hamiltonian, i.e. δsA(x) = δ〈kA(x)〉. Here the contour functions sA(x) and kA(x) capture the contribution from the degrees of freedom at x to SA and KA respectively. In some simple cases kA(x) is determined by the stress tensor. We also evaluate the quantum correction to the entanglement contour using the fine structure of the entanglement wedge and the additive linear combination (ALC) proposal for partial entanglement entropy (PEE) respectively. The fine structure picture shows that, the quantum correction to the boundary PEE can be identified as a bulk PEE of certain bulk region. While the ALC proposal shows that the quantum correction to the boundary PEE comes from the linear combination of bulk entanglement entropy. We focus on holographic theories with local modular Hamiltonian and configurations of quantum field theories where the ALC proposal applies.
Involved external institutions
How to cite
APA:
Han, M., & Wen, Q. (2021). First law and quantum correction for holographic entanglement contour. SciPost Physics, 11(3). https://doi.org/10.21468/SCIPOSTPHYS.11.3.058
MLA:
Han, Muxin, and Qiang Wen. "First law and quantum correction for holographic entanglement contour." SciPost Physics 11.3 (2021).
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China (CN)