Holographic R\'enyi Entropy and Generalized Entropy method

Miao Li; Wu-zhong Guo

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Holographic R\'enyi Entropy and Generalized Entropy method

Wu-zhong Guo, Miao Li

General Relativity and Quantum Cosmology · Submitted 11 Nov 2013

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The authors' main claim For a general entangling surface we derive the area law of entanglement entropy.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.83 · mentions code or data availability 0.02.

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In this paper we use the method of generalized gravitational entropy in \cite{Lewkowycz:2013nqa} to construct the dual bulk geometry for a spherical entangling surface, and calculate the R\'enyi entropy with the dual bulk gravity theory being either Einstein gravity or Lovelock gravity, this approach is closely related to that in \cite{Casini:2011kv}. For a general entangling surface we derive the area law of entanglement entropy. The area law is closely related with the local property of the entangling surface.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper we use the method of generalized gravitational entropy in \cite{Lewkowycz:2013nqa} to construct the dual bulk geometry for a spherical entangling surface, and calculate the R\'enyi entropy with the dual bulk gravity theory being either Einstein gravity or Lovelock gravity, this approach is closely related to that in \cite{Casini:2011kv}.	method 0.56	0.91	0.27	asserted 1.00
s1	For a general entangling surface we derive the area law of entanglement entropy.	result 0.93	0.93	0.36	asserted 1.00
s2	The area law is closely related with the local property of the entangling surface.	interpretation 0.90	0.48	0.16	asserted 1.00

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Original abstract

In this paper we use the method of generalized gravitational entropy in \cite{Lewkowycz:2013nqa} to construct the dual bulk geometry for a spherical entangling surface, and calculate the R\'enyi entropy with the dual bulk gravity theory being either Einstein gravity or Lovelock gravity, this approach is closely related to that in \cite{Casini:2011kv}. For a general entangling surface we derive the area law of entanglement entropy. The area law is closely related with the local property of the entangling surface.

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2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Contests 5 papers

This argument would lead to the proposal ([ref]) beyond the spherical shape [ref] [The subsequent papers [ref] [ref] point out there are some mismatches for higher derivative gravity theory, but the mismatch is removed by the paper [ref] ].

Towards a derivation of holographic entanglement entropy · Introduction · contest 0.71
This argument would lead to the proposal ([ref]) beyond the spherical shape [ref] [The subsequent papers [ref] [ref] point out there are some mismatches for higher derivative gravity theory, but the mismatch is removed by the paper [ref] ].

Entanglement entropy in higher derivative holography · Introduction · contest 0.71
This argument would lead to the proposal ([ref]) beyond the spherical shape [ref] [The subsequent papers [ref] [ref] point out there are some mismatches for higher derivative gravity theory, but the mismatch is removed by the paper [ref] ].

Note on generalized gravitational entropy in Lovelock gravity · Introduction · contest 0.71

Uses the method or tool of 1 paper

The generalized gravitational entropy [ref] provides us a method to study the entanglement entropy for a general entangling surface.

Generalized gravitational entropy · Introduction · 0.96

Compares with 2 papers

We find that the approach has a close relation with the previous one [ref] and confirm the relation between the reduced and the thermal states for the field theory.

Towards a derivation of holographic entanglement entropy · Discussion and Conclusion · 0.98
The entanglement entropy is [equation] the result is the same as in [ref] .

Holographic Calculations of Renyi Entropy · Lovelock gravity for arbitrary dimension · 1.00

Cites as support 1 paper

The approach in [ref] can be seen as evidence for the generalized gravitational entropy method.

Towards a derivation of holographic entanglement entropy · Relation between generalized entropy method and previous approach · 0.99

Cites as background 2 papers

Another interesting thing concerning the entanglement entropy is the the variance of entanglement entropy for excited state that is discussed in many paper recently, e.g., [ref] - [ref] .

Thermodynamical Property of Entanglement Entropy for Excited States · Discussion and Conclusion · 1.00
Another interesting thing concerning the entanglement entropy is the the variance of entanglement entropy for excited state that is discussed in many paper recently, e.g., [ref] - [ref] .

Entanglement Temperature in Non-conformal Cases · Discussion and Conclusion · 1.00

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