Entanglement entropy through conformal interfaces in the 2D Ising model

Brehm, Enrico M.; Brunner, Ilka

doi:10.1007/jhep09(2015)080

Cited by 47 publications

(89 citation statements)

References 50 publications

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“…This can be done for some excited states that have a natural left-right decomposition (see [20,21,22,23]) but it would be interesting to preform it for (5.1) even in known RCFTs.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Entanglement constant for conformal families

Caputa

Véliz-Osorio

2015

Phys. Rev. D

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We show that in 1+1 dimensional conformal field theories, exciting a state with a local operator increases the Rényi entanglement entropies by a constant which is the same for every member of the conformal family. Hence, it is an intrinsic parameter that characterises local operators from the perspective of quantum entanglement. In rational conformal field theories this constant corresponds to the logarithm of the quantum dimension of the primary operator. We provide several detailed examples for the second Rényi entropies and a general derivation.arXiv:1507.00582v2 [hep-th] 16 Sep 2015

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“…This can be done for some excited states that have a natural left-right decomposition (see [20,21,22,23]) but it would be interesting to preform it for (5.1) even in known RCFTs.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Entanglement constant for conformal families

Caputa

Véliz-Osorio

2015

Phys. Rev. D

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“…(1.2) and the expression of c eff were also obtained in a two dimensional Ising CFT. 24 Most recently, quantum entanglement across a conformal interface where several CFTs join together was studied. It was found that the entanglement entropy of a single CFT i , with other CFTs as the rest, also has the generic form in Eq.(1.2).…”

Section: Cft2mentioning

confidence: 99%

“…27, analytical results of both entanglement spectrum and entanglement entropy were derived, and the result on entanglement entropy was later confirmed in a CFT calculation. 24 A series of works were then stimulated, including entanglement entropy across quantum wire junctions, 28,29 and entanglement entropy across a conformal interface in bosonic quantum chains. 30 Interestingly, in Ref.…”

Section: Cft2mentioning

confidence: 99%

Entanglement evolution across a conformal interface

Wen

Wang

Ryu

2018

J. Phys. A: Math. Theor.

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For two dimensional conformal field theories in the ground state, it is known that a conformal interface along the entanglement cut can suppress the entanglement entropy from SA ∼ c log L to SA ∼ ceff log L, where L is the length of the subsystem A, and ceff ∈ [0, c] is the effective central charge which depends on the transmission property of the conformal interface. In this work, by making use of conformal mappings, we show that a conformal interface has the same effect on entanglement evolution in non-equilibrium cases, including global, local and certain inhomogeneous quantum quenches. I.e., a conformal interface suppresses the time evolution of entanglement entropy by effectively replacing the central charge c with ceff, where ceff is exactly the same as that in the ground state case. We confirm this conclusion by a numerical study on a critical fermion chain. Furthermore, based on the quasi-particle picture, we conjecture that this conclusion holds for an arbitrary quantum quench in CFTs, as long as the initial state can be described by a regularized conformal boundary state. arXiv:1711.02126v4 [cond-mat.str-el]

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“…In particular, we work out in detail the Ishibashi states corresponding to gapped edges and interfaces. The important new ingredients compared to previous works such as [7,8,9,10,11,12,13] are that we provide a careful treatment of the matching of anyon charges across the interface using tools in anyon condensation. The anyon condensation picture allows us to generalize the results to include cases with ground state degeneracies, and also to non-Abelian systems.…”

Section: Introductionmentioning

confidence: 99%

Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part I

Lou

Shen

Hung

2019

J. High Energ. Phys.

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In this paper, we study gapped edges/interfaces in a 2+1 dimensional bosonic topological order and investigate how the topological entanglement entropy is sensitive to them. We present a detailed analysis of the Ishibashi states describing these edges/interfaces making use of the physics of anyon condensation in the context of Abelian Chern-Simons theory, which is then generalized to more non-Abelian theories whose edge RCFTs are known. Then we apply these results to computing the entanglement entropy of different topological orders. We consider cases where the system resides on a cylinder with gapped boundaries and that the entanglement cut is parallel to the boundary. We also consider cases where the entanglement cut coincides with the interface on a cylinder. In either cases, we find that the topological entanglement entropy is determined by the anyon condensation pattern that characterizes the interface/boundary. We note that conditions are imposed on some non-universal parameters in the edge theory to ensure existence of the conformal interface, analogous to requiring rational ratios of radii of compact bosons.

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Entanglement entropy through conformal interfaces in the 2D Ising model

Cited by 47 publications

References 50 publications

Entanglement constant for conformal families

Entanglement constant for conformal families

Entanglement evolution across a conformal interface

Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part I

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