Holographic geometry of cMERA for quantum quenches and finite temperature

Mollabashi, Ali; Naozaki, Masahiro; Ryu, Shinsei; Takayanagi, Tadashi

doi:10.1007/jhep03(2014)098

Cited by 81 publications

(104 citation statements)

References 65 publications

(139 reference statements)

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“…7(a), we plot the evolution of the entanglement negativity with different (d, l) according to Eq. (45). A 'light-cone' effect can be observed: For t < d, there is no entanglement negativity between A 1 and A 2 .…”

Section: (B)mentioning

confidence: 97%

Entanglement negativity after a local quantum quench in conformal field theories

2015

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We study the time evolution of the entanglement negativity after a local quantum quench in (1+1)-dimensional conformal field theories (CFTs), which we introduce by suddenly joining two initially decoupled CFTs at their endpoints. We calculate the negativity evolution for both adjacent intervals and disjoint intervals explicitly. For two adjacent intervals, the entanglement negativity grows logarithmically in time right after the quench. After developing a plateau-like feature, the entanglement negativity drops to the ground-state value. For the case of two spatially separated intervals, a light-cone behavior is observed in the negativity evolution; in addition, a long-range entanglement, which is independent of the distance between two intervals, can be created. Our results agree with the heuristic picture that quasiparticles, which carry entanglement, are emitted from the joining point and propagate freely through the system. Our analytical results are confirmed by numerical calculations based on a critical harmonic chain.

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Section: (B)mentioning

confidence: 97%

Entanglement negativity after a local quantum quench in conformal field theories

2015

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“…Nevertheless, explicit formulations of cMERA are so far only available for free field theories [5] (see [7,8,20,21] for various studies) which is the opposite regime from the strongly interacting CFTs which possess gravity duals, the so-called holographic CFTs. A formal construction of cMERA for general CFTs can be found in [14,19].…”

Section: Jhep11(2017)097mentioning

confidence: 99%

“…So we simply ignore this. 8 In two dimensional CFTs, as we will explain in section 6, due to the conformal anomaly we actually need to define a relative complexity by the difference of the Liouville action between two different metrics. However this does not change out argument in this section.…”

Section: Jhep11(2017)097mentioning

confidence: 99%

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

Caputa

Kundu

Miyaji

et al. 2017

J. High Energ. Phys.

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281

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Abstract:We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.

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“…The quantum entanglement is expected to be an important quantity which may shed light on the mechanism behind the AdS/CFT correspondence, e.g., [8][9][10][11]. In particular, the entanglement on the boundary is expected to be related to gravity in bulk e.g., [12][13][14][15][16][17][18][19]. Therefore, it is important to reveal the fundamental properties of (Rényi) entanglement entropy.…”

Section: Contentsmentioning

confidence: 99%

Notes on quantum entanglement of local operators

Nozaki

2014

J. High Energ. Phys.

140

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This is an expanded version of the short report arXiv:1401.0539, where we studied the time evolution of (Renyi) entanglement entropies for the excited state defined by acting a given local operator on the ground state. In the present paper, we introduce (Renyi) entanglement entropies of given local operators which are defined by late time values of excesses of (Renyi) entanglement entropies. They measure the degrees of freedom of local operators and characterize them in conformal field theories from the viewpoint of quantum entanglement. We explain how to compute them in free massless scalar field theories and we also investigate their time evolution. Our results can be interpreted in terms of the relativistic propagation of entangled pairs. The main new results which we acquire in the present paper are as follows. Firstly, we provide an explanation which shows that (Renyi) entanglement entropies of a specific operator are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. That operator is constructed of only the scalar field. Secondly, we found the sum rule which (Renyi) entanglement entropies of those local operators obey. Those local operators are located separately. Moreover we argue that (Renyi) entanglement entropies of specific operators in conformal field theories are given by (Renyi) entanglement entropies whose reduced density matrices are given by the binomial distribution. These specific operators are constructed of single-species operators. We also argue that general operators obey the sum rule which we mentioned above.

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Holographic geometry of cMERA for quantum quenches and finite temperature

Cited by 81 publications

References 65 publications

Entanglement negativity after a local quantum quench in conformal field theories

Entanglement negativity after a local quantum quench in conformal field theories

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

Notes on quantum entanglement of local operators

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