Entanglement entropies in conformal systems with boundaries

Taddia, Luca; Xavier, J. C.; Alcaraz, Francisco C.; Sierra, Germȧn

doi:10.1103/physrevb.88.075112

Cited by 50 publications

(97 citation statements)

References 35 publications

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“…The contribution of the zero modes to the boundary state cancel the constant terms and factors powers of ǫ present in the Neumann case; a similar behavior was observed in [15]. Hence the entanglement entropy is only thermal.…”

Section: Jhep01(2015)110supporting

confidence: 67%

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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)110supporting

confidence: 67%

“…Boundary states in BCFT are generalizations of coherent states which are typical in quantum mechanics and quantum field theory. Various results have been obtained in the context of condensed matter [15], including also applications to the entanglement of topologically ordered states [16].…”

Section: Jhep01(2015)110mentioning

confidence: 99%

Left-right entanglement entropy of boundary states

Zayas

Quiroz

2015

J. High Energ. Phys.

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“…As for the Rényi entropies for two disjoint intervals in corresponding CFT, by employing known results about bosonization on higher genus Riemann surfaces for c = 1 models [31], the expression of F 2,n (x) for the Ising model can be written in terms of Riemann theta functions (2.8) evaluated for the period matrix τ 2 in (2.11). In particular, Trρ 15) where the sum is performed over all the possible characteristics e t ≡ (ε t , δ t ), being ε and δ two n − 1 dimensional vectors whose elements are either 0 or 1/2. Let us remark that in the sum (2.15) only the 2 n−2 (2 n−1 + 1) even characteristics occur.…”

Section: Mutual Informationmentioning

confidence: 99%

Entanglement entropy and negativity of disjoint intervals in CFT: some numerical extrapolations

Nobili¹,

Coser²,

Tonni³

2015

J. Stat. Mech.

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Abstract. The entanglement entropy and the logarithmic negativity can be computed in quantum field theory through a method based on the replica limit. Performing these analytic continuations in some cases is beyond our current knowledge, even for simple models. We employ a numerical method based on rational interpolations to extrapolate the entanglement entropy of two disjoint intervals for the conformal field theories given by the free compact boson and the Ising model. The case of three disjoint intervals is studied for the Ising model and the non compact free massless boson. For the latter model, the logarithmic negativity of two disjoint intervals has been also considered. Some of our findings have been checked against existing numerical results obtained from the corresponding lattice models.arXiv:1501.04311v1 [cond-mat.stat-mech]

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“…More generally, the entanglement entropy of excited states and, particularly, of coherent states has been recently discussed in the literature. Various results have been obtained in the context of condensed matter [5], including also applications to the entanglement of topologically ordered states [6].…”

Section: Introductionmentioning

confidence: 99%

Left-right entanglement entropy of Dp-branes

Zayas

Quiroz

2016

J. High Energ. Phys.

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Abstract:We compute the left-right entanglement entropy for Dp-branes in string theory. We employ the CFT approach to string theory Dp-branes, in particular, its presentation as coherent states of the closed string sector. The entanglement entropy is computed as the von Neumann entropy for a density matrix resulting from integration over the leftmoving degrees of freedom. We discuss various crucial ambiguities related to sums over spin structures and argue that different choices capture different physics; however, we advance a themodynamic argument that seems to favor a particular choice of replica. We also consider Dp branes on compact dimensions and verify that the effects of T-duality act covariantly on the Dp brane entanglement entropy. We find that generically the left-right entanglement entropy provides a suitable generalization of boundary entropy and of the D-brane tension.

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Entanglement entropies in conformal systems with boundaries

Cited by 50 publications

References 35 publications

Left-right entanglement entropy of boundary states

Left-right entanglement entropy of boundary states

Entanglement entropy and negativity of disjoint intervals in CFT: some numerical extrapolations

Left-right entanglement entropy of Dp-branes

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