Relating bulk to boundary entanglement

Berthiere, Clément; Witczak-Krempa, William

doi:10.1103/physrevb.100.235112

Cited by 20 publications

(13 citation statements)

References 77 publications

(192 reference statements)

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“…There are also attempts to calculate the entanglement entropies for disconnected regions using (31). For example, naively taking a uniform cutoff for all the endpoints of multiintervals in CFT 2 will give [18,57] the results of Refs. [30,[41][42][43], which are not correct in general.…”

Section: Discussionmentioning

confidence: 99%

Formulas for partial entanglement entropy

Wen

2020

Phys. Rev. Research

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The partial entanglement entropy (PEE) s A (A i) characterizes how much the subset A i of A contribute to the entanglement entropy S A. We find one additional physical requirement for s A (A i), which is the invariance under a permutation. The partial entanglement entropy proposal satisfies all the physical requirements. We show that for Poincaré invariant theories the physical requirements are enough to uniquely determine the PEE (or the entanglement contour) to satisfy a general formula. This is the first time we find the PEE can be uniquely determined. Since the solution of the requirements is unique and the PEE proposal is a solution, the PEE proposal is justified for Poincaré invariant theories.

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Section: Discussionmentioning

confidence: 99%

Formulas for partial entanglement entropy

Wen

2020

Phys. Rev. Research

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“…In d = 4, the free energy on a hemisphere [15] (suitably normalized by the round 4-sphere free energy) was proposed and checked in free and perturbative examples to decrease under boundary RG flows. The boundary trace anomaly is also related to the entanglement entropy in the presence of a boundary which has been discussed in [21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

CFT in AdS and boundary RG flows

Giombi

Khanchandani

2020

J. High Energ. Phys.

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Using the fact that flat space with a boundary is related by a Weyl transformation to anti-de Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation functions of local operators, a quantity of interest is the free energy of the CFT computed on the AdS space with hyperbolic ball metric, i.e. with a spherical boundary. It is natural to expect that the AdS free energy can be used to define a quantity that decreases under boundary renormalization group flows. We test this idea by discussing in detail the case of the large N critical O(N) model in general dimension d, as well as its perturbative descriptions in the epsilon-expansion. Using the AdS approach, we recover the various known boundary critical behaviors of the model, and we compute the free energy for each boundary fixed point, finding results which are consistent with the conjectured F-theorem in a continuous range of dimensions. Finally, we also use the AdS setup to compute correlation functions and extract some of the BCFT data. In particular, we show that using the bulk equations of motion, in conjunction with crossing symmetry, gives an efficient way to constrain bulk two-point functions and extract anomalous dimensions of boundary operators.

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“…Note that this evaluation of entanglement entropy using PEE is very subtle for disconnected regions.For example, previous studies[14,51,56] showed that naively taking an uniform cutoff for all the endpoints of multi-intervals in CFT2 will give the results of refs [57][58][59][60],. which is only justified for free fermions while incorrect in more general theories.…”

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confidence: 99%

Balanced partial entanglement and the entanglement wedge cross section

Wen

2021

J. High Energ. Phys.

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In this article we define a new information theoretical quantity for any bipartite mixed state ρAB. We call it the balanced partial entanglement (BPE). The BPE is the partial entanglement entropy, which is an integral of the entanglement contour in a subregion, that satisfies certain balance requirements. The BPE depends on the purification hence is not intrinsic. However, the BPE could be a useful way to classify the purifications. We discuss the entropy relations satisfied by BPE and find they are quite similar to those satisfied by the entanglement of purification. We show that in holographic CFT2 the BPE equals to the area of the entanglement wedge cross section (EWCS) divided by 4G. More interestingly, when we consider the canonical purification the BPE is just half of the reflected entropy, which also directly relate to the EWCS. The BPE can be considered as an generalization of the reflected entropy for a generic purification of the mixed state ρAB. We interpret the correspondence between the BPE and EWCS using the holographic picture of the entanglement contour.

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Relating bulk to boundary entanglement

Cited by 20 publications

References 77 publications

Formulas for partial entanglement entropy

Formulas for partial entanglement entropy

CFT in AdS and boundary RG flows

Balanced partial entanglement and the entanglement wedge cross section

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