Comments on defining entanglement entropy

Lin, Jennifer; Radičević, Đorđe

doi:10.1016/j.nuclphysb.2020.115118

Cited by 53 publications

(44 citation statements)

References 40 publications

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“…We will find that two of these definitions -the extended Hilbert space definition and the so-called "algebraic" definition -differ by a term proportional to L, hence yielding the same answer for the term S topo . This calculation corrects a comment made by [24] and repeated elsewhere [17,27], in the context of lattice gauge theories, stating that only one of these two definitions correctly reproduces the topological entanglement entropy. 12 (The quantum double model coincides with the weakly coupled limit of a lattice gauge theory.…”

Section: S(ρsupporting

confidence: 85%

Kitaev's quantum double model as an error correcting code

Cui

Ding

Han

et al. 2020

Quantum

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Kitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum error-correcting code. We offer an explicit proof that this is the case for arbitrary finite groups. Actually a stronger claim is shown: any two states with zero energy density in some contractible region must have the same reduced state in that region. Alternatively, the local properties of a gauge-invariant state are fully determined by specifying that its holonomies in the region are trivial. We contrast this result with the fact that local properties of gauge-invariant states are not generally determined by specifying all of their non-Abelian fluxes --- that is, the Wilson loops of lattice gauge theory do not form a complete commuting set of observables. We also note that the methods developed by P. Naaijkens (PhD thesis, 2012) under a different context can be adapted to provide another proof of the error correcting property of Kitaev's model. Finally, we compute the topological entanglement entropy in Kitaev's model, and show, contrary to previous claims in the literature, that it does not depend on whether the ``log dim R'' term is included in the definition of entanglement entropy.

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Section: S(ρsupporting

confidence: 85%

Kitaev's quantum double model as an error correcting code

Cui

Ding

Han

et al. 2020

Quantum

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“…There have also been efforts to characterize, for local subsystems, the most general boundary symmetry algebras spanned by the edge modes [14][15][16][17][18][19][20][21], with potentially important consequences for quantum gravity [22,23]. Another important development at finite distance has been the realization that a proper treatment of the edge modes is crucial even when dealing with fictitious entangling interfaces, which has consequences in the computations of entanglement entropy [24][25][26][27][28][29][30][31][32][33][34]. At infinity on the other hand, a lot of work has been dedicated towards understanding the intricate infrared properties of theories with massless excitations, and there a central role is played by large gauge transformations and soft modes [35].…”

Section: Jhep09(2020)134mentioning

confidence: 99%

“…On a spatial hypersurface, the physical phase space and Hilbert space of a gauge theory both fail to be factorizable due to the presence of the gauge constraints 2 and the resulting inherent non-locality of gauge-invariant observables. Aside from being a conceptual issue for the JHEP09(2020)134 definition of local subsystems [15], this also represents an a priori technical obstruction to computing quantities such as the entanglement entropy of gauge fields across a fictitious interface between two regions [33]. This difficulty can however be bypassed by resorting to a so-called extended Hilbert space.…”

Section: Jhep09(2020)134mentioning

confidence: 99%

“…The computation of this latter being a notoriously subtle issue, a more precise statement is that there exist many ways of computing entanglement entropy (giving the same result but using different technical routes and tools, see e.g. [33]), with only some of these making manifest the role of the edge modes. In lattice gauge theory, the contribution of the edge modes of the extended Hilbert space to the entanglement entropy was noted in [25,41].…”

Section: Jhep09(2020)134mentioning

confidence: 99%

“…This effort is pushing forward and shedding new light onto ideas which have been around for a long time in condensed matter, pure gauge theory, and the study of black hole entropy [5,55,73,76,107], but whose generality has perhaps not yet been fully appreciated. In particular, this has highlighted the important role of edge states in the definition of entanglement entropy [24,25,33,37], their relationship with the infrared properties of massless theories [32,35,108], and has unraveled rich examples of boundary symmetries and dynamics in the gravitational context [3, 14-16, 20, 109]. In spite of these remarquable developments, we believe that there is still no unified treatment for describing how exactly the edge modes arise (in relation to e.g.…”

Section: Jhep09(2020)134mentioning

confidence: 99%

See 2 more Smart Citations

Extended actions, dynamics of edge modes, and entanglement entropy

Geiller

Jai-akson

2020

J. High Energ. Phys.

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In this work we propose a simple and systematic framework for including edge modes in gauge theories on manifolds with boundaries. We argue that this is necessary in order to achieve the factorizability of the path integral, the Hilbert space and the phase space, and that it explains how edge modes acquire a boundary dynamics and can contribute to observables such as the entanglement entropy. Our construction starts with a boundary action containing edge modes. In the case of Maxwell theory for example this is equivalent to coupling the gauge field to boundary sources in order to be able to factorize the theory between subregions. We then introduce a new variational principle which produces a systematic boundary contribution to the symplectic structure, and thereby provides a covariant realization of the extended phase space constructions which have appeared previously in the literature. When considering the path integral for the extended bulk + boundary action, integrating out the bulk degrees of freedom with chosen boundary conditions produces a residual boundary dynamics for the edge modes, in agreement with recent observations concerning the contribution of edge modes to the entanglement entropy. We put our proposal to the test with the familiar examples of Chern-Simons and BF theory, and show that it leads to consistent results. This therefore leads us to conjecture that this mechanism is generically true for any gauge theory, which can therefore all be expected to posses a boundary dynamics. We expect to be able to eventually apply this formalism to gravitational theories.

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Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions

Anninos

Denef

Law

et al. 2022

J. High Energ. Phys.

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Motivated by the prospect of constraining microscopic models, we calculate the exact one-loop corrected de Sitter entropy (the logarithm of the sphere partition function) for every effective field theory of quantum gravity, with particles in arbitrary spin representations. In doing so, we universally relate the sphere partition function to the quotient of a quasi-canonical bulk and a Euclidean edge partition function, given by integrals of characters encoding the bulk and edge spectrum of the observable universe. Expanding the bulk character splits the bulk (entanglement) entropy into quasinormal mode (quasiqubit) contributions. For 3D higher-spin gravity formulated as an sl(n) Chern-Simons theory, we obtain all-loop exact results. Further to this, we show that the theory has an exponentially large landscape of de Sitter vacua with quantum entropy given by the absolute value squared of a topological string partition function. For generic higher-spin gravity, the formalism succinctly relates dS, AdS± and conformal results. Holography is exhibited in quasi-exact bulk-edge cancelation.

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Comments on defining entanglement entropy

Cited by 53 publications

References 40 publications

Kitaev's quantum double model as an error correcting code

Kitaev's quantum double model as an error correcting code

Extended actions, dynamics of edge modes, and entanglement entropy

Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions

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