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How robust is the entanglement entropy-area relation?
General Relativity and Quantum Cosmology · Submitted 12 Nov 2005
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This suggests that for large horizons, the ground state entropy dominates, whereas entropy due to excited states gives power law corrections.
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The abstract, sentence by sentence
We revisit the problem of finding the entanglement entropy of a scalar field on a lattice by tracing over its degrees of freedom inside a sphere. It is known that this entropy satisfies the area law -- entropy proportional to the area of the sphere -- when the field is assumed to be in its ground state. We show that the area law continues to hold when the scalar field degrees of freedom are in generic coherent states and a class of squeezed states. However, when excited states are considered, the entropy scales as a lower power of the area. This suggests that for large horizons, the ground state entropy dominates, whereas entropy due to excited states gives power law corrections. We discuss possible implications of this result to black hole entropy.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We revisit the problem of finding the entanglement entropy of a scalar field on a lattice by tracing over its degrees of freedom inside a sphere. | contribution 0.55 | 0.81 | 0.02 | asserted 0.58 |
| s1 | It is known that this entropy satisfies the area law -- entropy proportional to the area of the sphere -- when the field is assumed to be in its ground state. | background 1.00 | 0.04 | 0.05 | asserted 1.00 |
| s2 | We show that the area law continues to hold when the scalar field degrees of freedom are in generic coherent states and a class of squeezed states. | result 0.99 | 0.95 | 0.49 | asserted 1.00 |
| s3 | However, when excited states are considered, the entropy scales as a lower power of the area. | result 0.99 | 0.88 | 0.27 | asserted 1.00 |
| s4 | This suggests that for large horizons, the ground state entropy dominates, whereas entropy due to excited states gives power law corrections. | interpretation 1.00 | 0.57 | 0.31 | hedged possibility 1.00 |
| s5 | We discuss possible implications of this result to black hole entropy. | interpretation 0.88 | 0.48 | 0.05 | unclear 0.74 |
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The paper
Original abstract
We revisit the problem of finding the entanglement entropy of a scalar field on a lattice by tracing over its degrees of freedom inside a sphere. It is known that this entropy satisfies the area law -- entropy proportional to the area of the sphere -- when the field is assumed to be in its ground state. We show that the area law continues to hold when the scalar field degrees of freedom are in generic coherent states and a class of squeezed states. However, when excited states are considered, the entropy scales as a lower power of the area. This suggests that for large horizons, the ground state entropy dominates, whereas entropy due to excited states gives power law corrections. We discuss possible implications of this result to black hole entropy.
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References
How the literature uses it
15 arXiv papers cite this in 41 sentences
Papers citing it · 29 sentences without a confident label
Builds on it 2 papers
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In order to determine which one is correct, it is imperative to investigate various generalizations of the scenarios considered in Ref. [ref] .
Power-law corrections to black-hole entropy via entanglement · Power law corrections to area · 0.80
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Extending the analysis of the earlier work [ref] , we have shown that for small black-hole areas the area law is violated not only when the oscillator modes that represent the scalar DoF are in ES, but also when they are in a linear superposition of GS and ES.
Power-law corrections to entanglement entropy of horizons · Conclusions · 1.00
Compares with it 1 paper
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The computations have been done with a precision[The computations here are one order of magnitude more accurate than those in Ref. [ref] ] of $0.01%$ for the set of values: $N = 300, n = 100 - 200$ and $o = 30, 40, 50$, $o$ being the last non-zero columns of the vector $^T$.
Power-law corrections to entanglement entropy of horizons · Entanglement entropy for a Superposition of GS and ES · 0.91
Cites it as background 8 papers
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In Appendix [ref] we briefly review the results obtained in the earlier works [ref] for the ground state and 1-particle state.
Power-law corrections to entanglement entropy of horizons · Introduction intro · 0.98
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(b) the other that associate $S__BH$ with quantum fields in a fixed BH background, like the brick-wall model [ref] , the quantum entanglement of modes inside and outside of the horizon [ref] and the Noether charge [ref] .
Black hole entropy from entanglement: A review · Introduction intro · 0.87
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In general, if we consider entanglement entropies, we expect the result to be divergent, i.e. the leading divergence is the so-called area term [ref] .
Entanglement entropy and $T\bar T$ deformations beyond antipodal points from holography · Renormalization and generalized entanglement entropies · 0.93
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