Informational properties of holographic Lifshitz field theory *

Gong, Huajie; Liu, Peng; Fu, Guoyang; Kuang, Xiao-Mei; Wu, Jian-Pin

doi:10.1088/1674-1137/abefca

Cited by 10 publications

(3 citation statements)

References 117 publications

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“…Meanwhile, a similar concept called holographic reflected entropy, which describes the entanglement involving the canonical purification of mixed states, has also been related to the EWCS [9]. EWCS, as a good measure of mixed state entanglement, has been widely studied in recent literature [9][10][11][12][13][14][15][16][17][18][19][20][21]. Similar to the holographic dual of entanglement entropy, the holographic dual of reflected entropy with quantum fields in the bulk is proposed as [9] S R (A : B) = min…”

Section: S(a) = Minmentioning

confidence: 99%

Reflected entropy in double holography

Ling

Liu

et al. 2022

J. High Energ. Phys.

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Recently, the reflected entropy is proposed in holographic approach to describe the entanglement of a bipartite quantum system in a mixed state, which is identified as the area of the reflected minimal surface inside the entanglement wedge. In this paper, we study the reflected entropy in the doubly holographic setup, which contains the degrees of freedom of quantum matter in the bulk. In this context, we propose a notion of quantum entanglement wedge cross-section, which may describe the reflected entropy with higher-order quantum corrections. We numerically compute the reflected entropy in pure AdS background and black hole background in four dimensions, respectively. In general, the reflected entropy contains the contribution from the geometry on the brane and the contribution from the CFT. We compute their proportion for different Newton constants and find that their behaviors are in agreement with the results based on the semi-classical gravity and the correlation of CFT coupled to the bath CFT.

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Section: S(a) = Minmentioning

confidence: 99%

Reflected entropy in double holography

Ling

Liu

et al. 2022

J. High Energ. Phys.

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“…A wealth of literature has appeared under the title AdS/CMT, which seeks to build a holographic dictionary between the strongly-coupled quantum field theories underlying these systems and gravitational theories (see, e.g., [1,[19][20][21][22]). This work has led to exciting connections between black hole physics and the thermal physics of strongly interacting condensed matter [22], new ways (see, e.g., [23]) of calculating entanglement entropy in Lifshitz field theories [24,25] and searching for universal properties of non-relativistic field theories [19]; it has also led to fields of research such as holographic superconductors [26] and holographic hydrodynamics [27].…”

Section: Introductionmentioning

confidence: 99%

Lifshitz symmetry: Lie algebras, spacetimes and particles

2023

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We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits (“particles”) of Lie groups generated by spatial rotations, temporal and spatial translations and an additional scalar generator. As a first step we classify Lie algebras of this type in arbitrary dimension. Among them is the prototypical Lifshitz algebra, which motivates this work and the name “Lifshitz Lie algebras”. We classify homogeneous spacetimes of Lifshitz Lie groups. Depending on the interpretation of the additional scalar generator, these spacetimes fall into three classes:1. (d+2)-dimensional Lifshitz spacetimes which have one additional holographic direction;2. (d+1)-dimensional Lifshitz-Weyl spacetimes which can be seen as the boundary geometry of the spacetimes in (1) and where the scalar generator is interpreted as an anisotropic dilation;3. and (d+1)-dimensional aristotelian spacetimes with one scalar charge, including exotic fracton-like symmetries that generalise multipole algebras.We also classify the possible central extensions of Lifshitz Lie algebras and we discuss the homogeneous symplectic manifolds of Lifshitz Lie groups in terms of coadjoint orbits.

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“…For example, the Rényi entropy has been proposed proportional to the JHEP08(2022)123 area of the minimum cosmic brane [22], which back-reacts on the background geometry. Meanwhile, the entanglement of purification, reflected entropy and the entanglement negativity have all been related to the minimum cross-section in the entanglement wedge (EWCS) [23][24][25][26][27][28][29][30][31][32]. In addition, quantum complexity has been proposed proportional to the volume or the action of a certain region, that can capture quantum information other than the entanglement [33].…”

Section: Introductionmentioning

confidence: 99%

Entanglement wedge minimum cross-section for holographic aether gravity

Chen

Xiong

Niu

et al. 2022

J. High Energ. Phys.

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We study the entanglement wedge cross-section (EWCS) in holographic Aether gravity theory, a gravity theory with Lorentz symmetry violation while keeping the general covariance intact. We find that only a limited parameter space is allowed to obtain a black brane with positive Hawking temperature. Subject to these allowed parameter regions, we find that the EWCS could exhibit non-monotonic behaviors with system parameters. Meanwhile, the holographic entanglement entropy (HEE), and the corresponding mutual information (MI), can only exhibit monotonic behaviors. These phenomena suggest that the EWCS could capture much more rich content of the entanglement than that of the HEE and the MI. The role of the Lorentz violation in determining the behaviors of quantum information-related quantities is also analyzed.

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Informational properties of holographic Lifshitz field theory *

Cited by 10 publications

References 117 publications

Reflected entropy in double holography

Reflected entropy in double holography

Lifshitz symmetry: Lie algebras, spacetimes and particles

Entanglement wedge minimum cross-section for holographic aether gravity

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