Finiteness of entanglement entropy in collective field theory

Das, Sumit R.; Jevicki, Antal; Jun-jie, Zheng

doi:10.1007/jhep12(2022)052

Cited by 4 publications

(2 citation statements)

References 58 publications

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“…While finishing this paper, the work[79] appeared which discusses the finiteness of the entanglement entropy in matrix quantum mechanics. Their methods are different and the discussion is complementary.…”

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confidence: 99%

Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics

Ubaldo¹,

Policastro²

2023

Preprint

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We consider the generalization of a matrix integral with arbitrary spectral curve ρ 0 (E) to a 0+1D theory of matrix quantum mechanics (MQM). Using recent techniques for 1D quantum systems at large-N , we formulate a hydrodynamical effective theory for the eigenvalues. The result is a simple 2D free boson BCFT on a curved background, describing the quantum fluctuations of the eigenvalues around ρ 0 (E), which is now the large-N limit of the quantum expectation value of the eigenvalue density operator ρ(E). The average over the ensemble of random matrices becomes a quantum expectation value. Equal-time density correlations reproduce the results (including non-perturbative corrections) of random matrix theory. This suggests an interpretation of JT gravity as dual to a one-time-point reduction of MQM. As an application, we compute the Rényi entropy associated to a bipartition of the eigenvalues. We match a previous result by Hartnoll and Mazenc for the c = 1 matrix model dual to two-dimensional string theory and extend it to arbitrary ρ 0 (E). The hydrodynamical theory provides a clear picture of the emergence of spacetime in two dimensional string theory. The entropy is naturally finite and displays a large amount of short range entanglement, proportional to the microcanonical entropy. We also compute the reduced density matrix for a subset of n < N eigenvalues.

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mentioning

confidence: 99%

Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics

Ubaldo¹,

Policastro²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…While finishing this paper, the work[77] appeared which discusses the finiteness of the entanglement entropy in matrix quantum mechanics. Their methods are different and the discussion is complementary.…”

mentioning

confidence: 99%

Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics

Ubaldo

Policastro

2023

J. High Energ. Phys.

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We consider the generalization of a matrix integral with arbitrary spectral curve ρ0(E) to a 0+1D theory of matrix quantum mechanics (MQM). Using recent techniques for 1D quantum systems at large-N, we formulate a hydrodynamical effective theory for the eigenvalues. The result is a simple 2D free boson BCFT on a curved background, describing the quantum fluctuations of the eigenvalues around ρ0(E), which is now the large-N limit of the quantum expectation value of the eigenvalue density operator $$ \hat{\rho}(E) $$ ρ ̂ E .The average over the ensemble of random matrices becomes a quantum expectation value. Equal-time density correlations reproduce the results (including non-perturbative corrections) of random matrix theory. This suggests an interpretation of JT gravity as dual to a one-time-point reduction of MQM.As an application, we compute the Rényi entropy associated to a bipartition of the eigenvalues. We match a previous result by Hartnoll and Mazenc for the c = 1 matrix model dual to two-dimensional string theory and extend it to arbitrary ρ0(E). The hydrodynamical theory provides a clear picture of the emergence of spacetime in two dimensional string theory. The entropy is naturally finite and displays a large amount of short range entanglement, proportional to the microcanonical entropy. We also compute the reduced density matrix for a subset of n < N eigenvalues.

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Entanglement entropy in internal spaces and Ryu-Takayanagi surfaces

Das

Kaushal

Mandal

et al. 2023

J. High Energ. Phys.

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We study minimum area surfaces associated with a region, R, of an internal space. For example, for a warped product involving an asymptotically AdS space and an internal space K, the region R lies in K and the surface ends on ∂R. We find that the result of Graham and Karch can be avoided in the presence of warping, and such surfaces can sometimes exist for a general region R. When such a warped product geometry arises in the IR from a higher dimensional asymptotic AdS, we argue that the area of the surface can be related to the entropy arising from entanglement of internal degrees of freedom of the boundary theory. We study several examples, including warped or direct products involving AdS2, or higher dimensional AdS spaces, with the internal space, K = Rm, Sm; Dp brane geometries and their near horizon limits; and several geometries with a UV cut-off. We find that such RT surfaces often exist and can be useful probes of the system, revealing information about finite length correlations, thermodynamics and entanglement. We also make some preliminary observations about the role such surfaces can play in bulk reconstruction, and their relation to subalgebras of observables in the boundary theory.

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Finiteness of entanglement entropy in collective field theory

Cited by 4 publications

References 58 publications

Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics

Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics

Ensemble averaging in JT gravity from entanglement in Matrix Quantum Mechanics

Entanglement entropy in internal spaces and Ryu-Takayanagi surfaces

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