Is entanglement entropy proportional to area?

Ahmadi, Morteza; Das, Saurya; Shankaranarayanan, S.

doi:10.1139/p06-002

Cited by 14 publications

(20 citation statements)

References 11 publications

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“…general coherent states of two coupled harmonic oscillators is the same as that of the ground state [19,20], quite surprisingly. It is possible to argue, a posteriori, that the coherent states are, in the sense of the uncertainty principle, very classical and, therefore, do not contribute to quantum entanglement beyond that already present in the vacuum state.…”

Section: Jhep01(2015)110mentioning

confidence: 84%

“…First, one would like to understand some simple excited states such as: low excited states and eventually coherent states. For the case of harmonic oscillators some low excited states and their entanglement entropy were considered in [19,20]; our interest is centered on coherent states. In the case of quantum mechanics, a coherent state of a harmonic oscillator can be defined as an eigenstate of the annihilation operator.…”

Section: Coupled Harmonic Oscillators: Beyond the Ground Statementioning

confidence: 99%

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Left-right entanglement entropy of boundary states

Zayas

Quiroz

2015

J. High Energ. Phys.

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Abstract:We study entanglement entropy of boundary states in a free bosonic conformal field theory. A boundary state can be thought of as composed of a particular combination of left and right-moving modes of the two-dimensional conformal field theory. We investigate the reduced density matrix obtained by tracing over the right-moving modes in various boundary states. We consider Dirichlet and Neumann boundary states of a free noncompact as well as a compact boson. The results for the entanglement entropy indicate that the reduced system can be viewed as a thermal CFT gas. Our findings are in agreement and generalize results in quantum mechanics and quantum field theory where coherent states can also be considered. In the compact case we verify that the entanglement entropy expressions are consistent with T-duality.

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Section: Jhep01(2015)110mentioning

confidence: 84%

Section: Coupled Harmonic Oscillators: Beyond the Ground Statementioning

confidence: 99%

Left-right entanglement entropy of boundary states

Zayas

Quiroz

2015

J. High Energ. Phys.

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“…In this case, we consider one HO is in the excited state while the rest N ÿ 1 are in their GS [13,14]. From Eq.…”

Section: First Excited Statementioning

confidence: 99%

Power-law corrections to entanglement entropy of horizons

2008

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We reexamine the idea that the origin of black-hole entropy may lie in the entanglement of quantum fields between the inside and outside of the horizon. Motivated by the observation that certain modes of gravitational fluctuations in a black-hole background behave as scalar fields, we compute the entanglement entropy of such a field, by tracing over its degrees of freedom inside a sphere. We show that while this entropy is proportional to the area of the sphere when the field is in its ground state, a correction term proportional to a fractional power of area results when the field is in a superposition of ground and excited states. The area law is thus recovered for large areas. Further, we identify the location of the degrees of freedom that give rise to the above entropy.

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“…However, a crucial assumption was made in the analyses of [4] and [5], that all the harmonic oscillators (HOs) -resulting from the descretization of the scalar fieldare in their ground state (GS). Thus the natural question which one would ask is: How sensitive is the area law to the choice of the quantum state of the HOs?In a recent paper, the current authors had investigated this problem for a simpler system of two coupled oscillators, and found two interesting results [8]: (i) the entropy remains unchanged if the GS oscillator wave functions are replaced by generalized coherent states (GCS), and (ii) the entropy could increase substantially (as much as 50%) even if one of the oscillators is in its first excited state (ES). This raises the possibility that for the more interesting case of N -coupled oscillators (modeling a free scalar field), deviations from the area law could result if excited states are taken into account.…”

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confidence: 99%

How robust is the entanglement entropy-area relation?

2006

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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 lawentropy 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. Although classical black holes (BHs) have infinite entropy and zero temperature, Bekenstein -inspired by the area increase theorem of general relativity -proposed that BHs have entropy proportional to horizon area A H . This, together with Hawking's discovery that BHs radiate with the temperature T H = c 3 /(8πGM ) have given rise to the Bekenstein-Hawking area law for BH entropy:The area (as opposed to volume) proportionality of BH entropy has been an intriguing issue for decades. Attempts to understand this problem can be broadly classified into two classes: (i) those that count fundamental states such as D-Branes and spin-networks, which are supposed to model BHs [3], and (ii) those that study entanglement entropy [4,5] and its variants such as the brick-wall model and Shakarov's induced gravity [6].In the case of entanglement entropy, which is of interest in this work, it is assumed that the von Neumann entropyof quantum fields due to correlations between the exterior and interior of the BH horizon, accounts for black hole entropy. Such correlations imply that the state of field, when restricted outside the horizon, is mixed, although the full state may be pure [4,5]. Although this entropy is ultra-violet divergent, a suitable short distance cut-off [O(ℓ P )] gives S ∝ A H (it was argued in [4] that this entropy must be formally divergent). This idea gained further credence, when it was shown that even for Minkowski space-time (MST), tracing over the degrees of freedom inside a hypothetical sphere (of radius R), gives rise to the entropy of the form 0.3 (R/a) 2 where a is the lattice spacing [4,5] (it was shown in [7] that quantum fluctuations inside the sub-volume scale as its bounding area as well). Thus, the area-law may be a direct consequence of entanglement alone. However, a crucial assumption was made in the analyses of [4] and [5], that all the harmonic oscillators (HOs) -resulting from the descretization of the scalar fieldare in their ground state (GS). Thus the natural question which one would ask is: How sensitive is the area law to the choice of the quantum state of the HOs?In a recent paper, the current authors had investigated this problem for a simpler system of two coupled oscillators, and found two interesting results [8]: (i) the entropy remains unch...

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Is entanglement entropy proportional to area?

Cited by 14 publications

References 11 publications

Left-right entanglement entropy of boundary states

Left-right entanglement entropy of boundary states

Power-law corrections to entanglement entropy of horizons

How robust is the entanglement entropy-area relation?

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