Chaos in quantum channels

Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; Yoshida, Beni

doi:10.1007/jhep02(2016)004

Cited by 655 publications

(900 citation statements)

References 74 publications

(277 reference statements)

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“…Given a boundary region A containing a number of open links of the tensor network, the entanglement entropy of the tensor network in each of the above approaches reproduces an analog of the RT formula (See e.g. [37][38][39][40][41][42][43][44][45][46] for some more recent developments)…”

Section: Jhep11(2017)148mentioning

confidence: 99%

Discrete gravity on random tensor network and holographic Rényi entropy

Han

Huang

2017

J. High Energ. Phys.

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In this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body quantum state |Ψ using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement Rényi entropy of |Ψ is shown to holographically relate to the on-shell action of Einstein gravity on a branch cover bulk manifold. The resulting Rényi entropy S n of |Ψ approximates with high precision the Rényi entropy of ground state in 2-dimensional conformal field theory (CFT). In particular it reproduces the correct n dependence. Our results develop the framework of realizing the AdS 3 /CFT 2 correspondence on random tensor networks, and provide a new proposal to approximate the CFT ground state.

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Section: Jhep11(2017)148mentioning

confidence: 99%

Discrete gravity on random tensor network and holographic Rényi entropy

Han

Huang

2017

J. High Energ. Phys.

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“…This allows us to connect analytically the free UV theory to the interacting and nearly conformal IR theory. Further recent work in this or similar models includes [14,15,16,17,7,18,19]. See also [20,21] for a string motivated model with disorder.…”

Section: Introductionmentioning

confidence: 99%

Remarks on the Sachdev-Ye-Kitaev model

2016

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We study a quantum mechanical model proposed by Sachdev, Ye and Kitaev. The model consists of N Majorana fermions with random interactions of a few fermions at a time. It it tractable in the large N limit, where the classical variable is a bilocal fermion bilinear. The model becomes strongly interacting at low energies where it develops an emergent conformal symmetry. We study two and four point functions of the fundamental fermions. This provides the spectrum of physical excitations for the bilocal field.The emergent conformal symmetry is a reparametrization symmetry, which is spontaneously broken to SL(2, R), leading to zero modes. These zero modes are lifted by a small residual explicit breaking, which produces an enhanced contribution to the four point function. This contribution displays a maximal Lyapunov exponent in the chaos region (out of time ordered correlator). We expect these features to be universal properties of large N quantum mechanics systems with emergent reparametrization symmetry.This article is largely based on talks given by Kitaev [1], which motivated us to work out the details of the ideas described there.

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“…Very importantly, as a characteristic velocity of a chaotic quantum system, v B sets a bound on the speed of the information propagation [1]. In holographic theories, the butterfly effect has extensively been studied in context [5][6][7][8][9][10][11][12][13][14][15][16][17]. In the study of high energy scattering near horizon and information scrambling of black holes it is found that the butterfly effect ubiquitously exists and is signaled by a…”

Section: Introductionmentioning

confidence: 99%

Holographic butterfly effect at quantum critical points

Ling¹,

Liu²,

Wu³

2017

J. High Energ. Phys.

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When the Lyapunov exponent λ L in a quantum chaotic system saturates the bound λ L 2πk B T , it is proposed that this system has a holographic dual described by a gravity theory. In particular, the butterfly effect as a prominent phenomenon of chaos can ubiquitously exist in a black hole system characterized by a shockwave solution near the horizon. In this paper we propose that the butterfly velocity can be used to diagnose quantum phase transition (QPT) in holographic theories. We provide evidences for this proposal with an anisotropic holographic model exhibiting metal-insulator transitions (MIT), in which the derivatives of the butterfly velocity with respect to system parameters characterizes quantum critical points (QCP) with local extremes in zero temperature limit. We also point out that this proposal can be tested by experiments in the light of recent progress on the measurement of out-of-time-order correlation function (OTOC).

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Chaos in quantum channels

Cited by 655 publications

References 74 publications

Discrete gravity on random tensor network and holographic Rényi entropy

Discrete gravity on random tensor network and holographic Rényi entropy

Remarks on the Sachdev-Ye-Kitaev model

Holographic butterfly effect at quantum critical points

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