Entanglement entropy on a fuzzy sphere with a UV cutoff

Chen, Hong Zhe; Karczmarek, Joanna L.

doi:10.1007/jhep08(2018)154

Cited by 11 publications

(17 citation statements)

References 25 publications

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“…This transition from a volume law to an area law behaviour has also been observed in quantum field theory calculations [90][91][92] and has been understood as a result of the nonlocality inherent of non-commutative theories [93,94]. Very recently, the full cutoff dependence was studied in [95] which found an exact match with respect to the results previously obtained in the strong coupling regime through holography.…”

Section: )supporting

confidence: 67%

Chaos and entanglement spreading in a non-commutative gauge theory

Fischler

Jahnke

Pedraza

2018

J. High Energ. Phys.

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Holographic theories with classical gravity duals are maximally chaotic: they saturate a set of bounds on the spread of quantum information. In this paper we question whether non-locality can affect such bounds. Specifically, we consider the gravity dual of a prototypical theory with non-local interactions, namely, N " 4 non-commutative super Yang Mills. We construct shock waves geometries that correspond to perturbations of the thermofield double state with definite momentum and study several chaos related properties of the theory, including the butterfly velocity, the entanglement velocity, the scrambling time and the maximal Lyapunov exponent. The latter two are unaffected by the non-commutative parameter θ, however, both the butterfly and entanglement velocities increase with the strength of the noncommutativity. This implies that non-local interactions can enhance the effective light-cone for the transfer of quantum information, eluding previously conjectured bounds encountered in the context of local quantum field theory. We comment on a possible limitation on the retrieval of quantum information imposed by non-locality. arXiv:1808.10050v3 [hep-th] 15 Nov 2018 6 Conclusions and outlook 34 A Momentum space correlator and the butterfly velocity 36 B Shock wave parameter α as a function of r 0 38 C Divergence of K 3 pr 0 q 39 -1 -

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Section: )supporting

confidence: 67%

Chaos and entanglement spreading in a non-commutative gauge theory

Fischler

Jahnke

Pedraza

2018

J. High Energ. Phys.

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“…It might also be interesting to understand the connection of ideas presented in this paper with the studies of causality in string field theory [14,15,[47][48][49][50]. Another question of interest is the finite g s corrections -entanglement entropy in interacting, non-local theories potentially has an interesting cross-over behavior between area law and volume law depending on whether the subregion size is larger or small compared to the scale of non-locality [51][52][53][54]. It would be interesting to check whether open string theory exhibits this phenomenon, perhaps perturbatively in g s .…”

Section: Discussionmentioning

confidence: 99%

Remarks on entanglement entropy in string theory

Balasubramanian

Parrikar

2018

Phys. Rev. D

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Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for Bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the "space of open string configurations". We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.

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“…The factor of N in (5.14) is due to the microscopic cutoff at a scale L fuzz ∼ L sph /N . Previous works on the entanglement of a free field on a fuzzy sphere involved similar wavefunctions but a different factorization of the Hilbert space, which was inspired instead by coherent states [61][62][63][64]. Those results did not always produce boundary-law entanglement.…”

Section: Fuzzy Sphere In the Mini-bmn Modelmentioning

confidence: 99%

Deep Quantum Geometry of Matrices

Han

Hartnoll

2020

Phys. Rev. X

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We employ machine learning techniques to provide accurate variational wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic matrices.Variational quantum Monte Carlo is implemented with deep generative flows to search for gauge invariant low energy states. The ground state, and also long-lived metastable states, of an SU(N ) matrix quantum mechanics with three bosonic matrices, as well as its supersymmetric 'mini-BMN' extension, are studied as a function of coupling and N .Known semiclassical fuzzy sphere states are recovered, and the collapse of these geometries in more strongly quantum regimes is probed using the variational wavefunction.We then describe a factorization of the quantum mechanical Hilbert space that corresponds to a spatial partition of the emergent geometry. Under this partition, the fuzzy sphere states show a boundary-law entanglement entropy in the large N limit.

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Entanglement entropy on a fuzzy sphere with a UV cutoff

Cited by 11 publications

References 25 publications

Chaos and entanglement spreading in a non-commutative gauge theory

Chaos and entanglement spreading in a non-commutative gauge theory

Remarks on entanglement entropy in string theory

Deep Quantum Geometry of Matrices

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