Microscopic model of quantum butterfly effect: Out-of-time-order correlators and traveling combustion waves

Aleǐner, I. L.; Faoro, Lara; Ioffe, L. B.

doi:10.1016/j.aop.2016.09.006

Cited by 250 publications

(329 citation statements)

References 43 publications

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“…3 While this connection between transport properties and chaos was first proposed in the holographic models, it has been also observed in condensed matter systems [14,[16][17][18]. 4 In [23], it was also shown that the diffusion constant may vanish across the phase transition, implying a dynamical transition to an many-body localization phase.…”

Section: Jhep06(2017)030mentioning

confidence: 99%

Diffusion and butterfly velocity at finite density

Niu

Kim

2017

J. High Energ. Phys.

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Abstract:We study diffusion and butterfly velocity (v B ) in two holographic models, linear axion and axion-dilaton model, with a momentum relaxation parameter (β) at finite density or chemical potential (µ). Axion-dilaton model is particularly interesting since it shows linear-T -resistivity, which may have something to do with the universal bound of diffusion. At finite density, there are two diffusion constants D ± describing the coupled diffusion of charge and energy. By computing D ± exactly, we find that in the incoherent regime (β/T 1, β/µ 1) D + is identified with the charge diffusion constant (D c ) and D − is identified with the energy diffusion constant (D e ). In the coherent regime, at very small density, D ± are 'maximally' mixed in the sense that D + (D − ) is identified with D e (D c ), which is opposite to the case in the incoherent regime. In the incoherent regime D e ∼ C − v 2 B /k B T where C − = 1/2 or 1 so it is universal independently of β and µ. However, D c ∼ C + v 2 B /k B T where C + = 1 or β 2 /16π 2 T 2 so, in general, C + may not saturate to the lower bound in the incoherent regime, which suggests that the characteristic velocity for charge diffusion may not be the butterfly velocity. We find that the finite density does not affect the diffusion property at zero density in the incoherent regime.

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Section: Jhep06(2017)030mentioning

confidence: 99%

Diffusion and butterfly velocity at finite density

Niu

Kim

2017

J. High Energ. Phys.

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“…[17]. In this work a relation between the entanglement entropy growth and the spreading of the OTOC was also conjectured [17] (c.f. Ref.…”

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confidence: 95%

Information propagation in isolated quantum systems

2017

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Entanglement growth and out-of-time-order correlators (OTOC) are used to assess the propagation of information in isolated quantum systems. In this work, using large scale exact time-evolution we show that for weakly disordered nonintegrable systems information propagates behind a ballistically moving front, and the entanglement entropy growths linearly in time. For stronger disorder the motion of the information front is algebraic and sub-ballistic and is characterized by an exponent which depends on the strength of the disorder, similarly to the sublinear growth of the entanglement entropy. We show that the dynamical exponent associated with the information front coincides with the exponent of the growth of the entanglement entropy for both weak and strong disorder. We also demonstrate that the temporal dependence of the OTOC is characterized by a fast nonexponential growth, followed by a slow saturation after the passage of the information front. Finally,we discuss the implications of this behavioral change on the growth of the entanglement entropy.Introduction. -While the speed of light is the absolute upper limit of information propagation in both classical and quantum relativistic systems, surprisingly a velocity which plays a similar role exists also for shortrange interacting nonrelativistic quantum systems. This velocity, known as the Lieb-Robinson velocity, bounds the spreading of correlations in the system and implies that information about local initial excitations propagates within a causal "light-cone", similarly to the lightcone encountered in the theory of special relativity [1]. The shape of the light-cone can be obtained from the correlation function

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“…(1.8) which diagnoses the quantum butterfly effect [22][23][24][25] and has been applied to various models recently [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. There are also experimental measurements of OTOC in different systems [43,44].…”

Section: Jhep07(2017)150mentioning

confidence: 99%

Tunable quantum chaos in the Sachdev-Ye-Kitaev model coupled to a thermal bath

Chen

Zhai

Zhang

2017

J. High Energ. Phys.

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The Sachdev-Ye-Kitaev (SYK) model describes Majorana fermions with random interaction, which displays many interesting properties such as non-Fermi liquid behavior, quantum chaos, emergent conformal symmetry and holographic duality. Here we consider a SYK model or a chain of SYK models with N Majorana fermion modes coupled to another SYK model with N 2 Majorana fermion modes, in which the latter has many more degrees of freedom and plays the role as a thermal bath. For a single SYK model coupled to the thermal bath, we show that although the Lyapunov exponent is still proportional to temperature, it monotonically decreases from 2π/β (β = 1/(k B T ), T is temperature) to zero as the coupling strength to the thermal bath increases. For a chain of SYK models, when they are uniformly coupled to the thermal bath, we show that the butterfly velocity displays a crossover from a √ T -dependence at relatively high temperature to a linear T -dependence at low temperature, with the crossover temperature also controlled by the coupling strength to the thermal bath. If only the end of the SYK chain is coupled to the thermal bath, the model can introduce a spatial dependence of both the Lyapunov exponent and the butterfly velocity. Our models provide canonical examples for the study of thermalization within chaotic models.

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Microscopic model of quantum butterfly effect: Out-of-time-order correlators and traveling combustion waves

Cited by 250 publications

References 43 publications

Diffusion and butterfly velocity at finite density

Diffusion and butterfly velocity at finite density

Information propagation in isolated quantum systems

Tunable quantum chaos in the Sachdev-Ye-Kitaev model coupled to a thermal bath

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