Entanglement as geometry and flow

Roy, Sudipto Singha; Santalla, Silvia N.; Rodríguez-Laguna, Javier; Sierra, Germȧn

doi:10.1103/physrevb.101.195134

Cited by 17 publications

(16 citation statements)

References 62 publications

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“…Recent explorations on entanglement contour or the PEE include [10][11][12][13][14][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. People propose formulas to construct the PEE (or entanglement contour) that satisfies the above requirements.…”

Section: Symmetry Under the Permutation: I(āmentioning

confidence: 99%

“…The third one is the partial entanglement entropy proposal [11,13] that claims the PEE is given by an additive linear combination of subset entanglement entropies. The fourth proposal [14] follows the construction of the extensive (or additive) mutual information (EMI) [54] (see also [51] for a related construction), which tried to solve the above seven requirements in CFT.…”

Section: Symmetry Under the Permutation: I(āmentioning

confidence: 99%

“…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%

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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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Section: Symmetry Under the Permutation: I(āmentioning

confidence: 99%

Section: Symmetry Under the Permutation: I(āmentioning

confidence: 99%

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confidence: 99%

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Balanced partial entanglement and the entanglement wedge cross section

Wen

2021

J. High Energ. Phys.

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“…Later we will call this proposal the ALC (additive linear combination) proposal for short 3 . The fourth proposal [21] follows the construction of the extensive (or additive) mutual information (EMI) [31] (see also [32] for a similar construction), which tried to solve the above seven requirements in CFT. The entanglement contour can also be studied under the picture of the bit threads [33] in holographic theories, see for example [19,[34][35][36].…”

Section: S a =mentioning

confidence: 99%

First law and quantum correction for holographic entanglement contour

Han

Wen²

2021

SciPost Phys.

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Entanglement entropy satisfies a first law-like relation, which equates the first order perturbation of the entanglement entropy for the region AA to the first order perturbation of the expectation value of the modular Hamiltonian, \delta S_{A}=\delta \langle K_A \rangleδSA=δ⟨KA⟩. We propose that this relation has a finer version which states that, the first order perturbation of the entanglement contour equals to the first order perturbation of the contour of the modular Hamiltonian, i.e. \delta s_{A}(\textbf{x})=\delta \langle k_{A}(\textbf{x})\rangleδsA(𝐱)=δ⟨kA(𝐱)⟩. Here the contour functions s_{A}(\textbf{x})sA(𝐱) and k_{A}(\textbf{x})kA(𝐱) capture the contribution from the degrees of freedom at \textbf{x}𝐱 to S_{A}SA and K_AKA respectively. In some simple cases k_{A}(\textbf{x})kA(𝐱) is determined by the stress tensor. We also evaluate the quantum correction to the entanglement contour using the fine structure of the entanglement wedge and the additive linear combination (ALC) proposal for partial entanglement entropy (PEE) respectively. The fine structure picture shows that, the quantum correction to the boundary PEE can be identified as a bulk PEE of certain bulk region. While the shows that the quantum correction to the boundary PEE comes from the linear combination of bulk entanglement entropy. We focus on holographic theories with local modular Hamiltonian and configurations of quantum field theories where the applies.

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“…Thus, given a quantum state, we are naturally led to the question: what is the geometry associated to its entanglement structure? A tentative answer to that question was provided by our group in [29], and we will build upon that work in order to provide a deeper insight.…”

Section: Introductionmentioning

confidence: 99%

Link representation of the entanglement entropies for all bipartitions

Roy

Santalla

Sierra

et al. 2021

J. Phys. A: Math. Theor.

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We have recently shown that the entanglement entropy of any bipartition of a quantum state can be approximated as the sum of certain link strengths connecting internal and external sites. The representation is useful to unveil the geometry associated with the entanglement structure of a quantum many-body state which may occasionally differ from the one suggested by the Hamiltonian of the system. Yet, the obtention of these entanglement links is a complex mathematical problem. In this work, we address this issue and propose several approximation techniques for matrix product states, free fermionic states, or in cases in which contiguous blocks are specially relevant. Along with this, we discuss the accuracy of the approximation for different types of states and partitions. Finally, we employ the link representation to discuss two different physical systems: the spin-1/2 long-range XXZ chain and the spin-1 bilinear biquadratic chain.

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Entanglement as geometry and flow

Cited by 17 publications

References 62 publications

Balanced partial entanglement and the entanglement wedge cross section

Balanced partial entanglement and the entanglement wedge cross section

First law and quantum correction for holographic entanglement contour

Link representation of the entanglement entropies for all bipartitions

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