Holographic butterfly effect at quantum critical points

Ling, Yi; Liu, Peng; Wu, Jian-Pin

doi:10.1007/jhep10(2017)025

Cited by 52 publications

(57 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This will be explored in [39]. This line of investigation could also make contact with the recent work on relating diffusion to a characteristic velocity extracted from the black hole horizon, related to out of time ordered correlators [40,41] and [13,[42][43][44][45][46][47][48][49][50]. Note added.-While writing up this work, Ref.…”

Section: Final Commentsmentioning

confidence: 89%

Diffusion in inhomogeneous media

2017

View full text Add to dashboard Cite

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. We analyze the retarded two-point functions involving the charges and the associated currents at long wavelengths, compared to the scale of the lattice, and, when the dc conductivities are finite, extract the hydrodynamic modes associated with diffusion of the charges. We show that the dispersion relations of these modes are related to the eigenvalues of a specific matrix constructed from the dc conductivities and certain thermodynamic susceptibilities, thus obtaining generalized Einstein relations. We illustrate these general results in the specific context of relativistic hydrodynamics where translation invariance is broken using spatially inhomogeneous and periodic deformations of the stress tensor and the conserved Uð1Þ currents. Equivalently, this corresponds to considering hydrodynamics on a curved manifold, with a spatially periodic metric and chemical potential, and we obtain the dispersion relations for the heat and charge diffusive modes.

show abstract

Section: Final Commentsmentioning

confidence: 89%

Diffusion in inhomogeneous media

2017

View full text Add to dashboard Cite

show abstract

“…For more details, we refer to [15,19,[37][38][39][40][41][42][43]. The butterfly effect as chaotic behaviour refers to the exponential growth of a small perturbation to a quantum system.…”

Section: Butterfly Velocitymentioning

confidence: 99%

Diffusion and butterfly velocity at finite density

Niu

Kim

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

“…Several experimental proposals have also appeared recently [33][34][35] that enable one to measure OTO correlators and scrambling and three preliminary experiments have already been carried out [36][37][38]. There has been a flurry of recent calculations of out-of-time order correlators in a variety of models [39][40][41][42][43][44][45][46][47][48][49][50][51]. There have also been some recent works exploring other formal aspects of these correlators, including fluctuation-dissipation-like theorems [52][53][54][55].…”

Section: ð1:2þmentioning

confidence: 99%

Onset of many-body chaos in the O(N) model

2017

View full text Add to dashboard Cite

The growth of commutators of initially commuting local operators diagnoses the onset of chaos in quantum many-body systems. We compute such commutators of local field operators with N components in the (2 þ 1)-dimensional OðNÞ nonlinear sigma model to leading order in 1=N. The system is taken to be in thermal equilibrium at a temperature T above the zero temperature quantum critical point separating the symmetry broken and unbroken phases. The commutator grows exponentially in time with a rate denoted λ L . At large N the growth of chaos as measured by λ L is slow because the model is weakly interacting, and we find λ L ≈ 3.2T=N. The scaling with temperature is dictated by conformal invariance of the underlying quantum critical point. We also show that operators grow ballistically in space with a "butterfly velocity" given by v B =c ≈ 1 where c is the Lorentz-invariant speed of particle excitations in the system. We briefly comment on the behavior of λ L and v B in the neighboring symmetry broken and unbroken phases.

show abstract

Holographic butterfly effect at quantum critical points

Cited by 52 publications

References 59 publications

Diffusion in inhomogeneous media

Diffusion in inhomogeneous media

Diffusion and butterfly velocity at finite density

Onset of many-body chaos in the O(N) model

Contact Info

Product

Resources

About