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arXiv:2401.04772 · Physical review. B./Physical review. B

Information scrambling and butterfly velocity in quantum spin glass chains

Venkata Lokesh K. Y., Surajit Bera, Sumilan Banerjee

Published Oct 4, 2024• 1 citation
arXivHTMLPDF

Abstract

Information scrambling may become enhanced for systems with many metastable configurations, such as glasses, when the complex dynamics samples the multitude of configurations. The authors study here the scrambling in chains of quantum dots, modeled via two paradigmatic spin glass models -- Sachdev-Ye and $p$-spin glass -- and show that the butterfly velocity characterizing scrambling is enhanced above the glass transition where the dynamics is maximally complex. However, the evolution of glassy complexity with quantum and thermal fluctuations in the two spin glasses is very different.

DOI
10.1103/physrevb.110.134202

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Information scrambling may become enhanced for systems with many metastable configurations, such as glasses, when the complex dynamics samples the multitude of configurations. The authors study here the scrambling in chains of quantum dots, modeled via two paradigmatic spin glass models -- Sachdev-Ye and ppp-spin glass -- and show that the butterfly velocity characterizing scrambling is enhanced above the glass transition where the dynamics is maximally complex. However, the evolution of glassy complexity with quantum and thermal fluctuations in the two spin glasses is very different.
The study of information scrambling in many-body systems has sharpened our understanding of quantum chaos, complexity, and gravity. Here, we extend the framework for exploring information scrambling to infinite-dimensional continuous variable (CV) systems. Unlike their discrete variable cousins, continuous variable systems exhibit two complementary domains of information scrambling: (i) scrambling in the phase space of a single mode and (ii) scrambling across multiple modes of a many-body system. Moreover, for each of these domains, we identify two distinct types of scrambling; genuine scrambling, where an initial operator localized in phase space spreads out, and quasiscrambling, where a local ensemble of operators distorts but the overall phase space volume remains fixed. To characterize these behaviors, we introduce a CV out-of-time-order correlation (OTOC) function based upon displacement operators and offer a number of results regarding the CV analog for unitary designs. Finally, we investigate operator spreading and entanglement growth in random local Gaussian circuits; to explain the observed behavior, we propose a simple hydrodynamical model that relates the butterfly velocity, the growth exponent, and the diffusion constant. Experimental realizations of continuous variable scrambling as well as its characterization using CV OTOCs will be discussed.
Abstract In this work, we study the information scrambling and the entanglement dynamics in the complex Brownian Sachdev-Ye-Kitaev (cBSYK) models, focusing on their dependence on the charge density n. We first derive the effective theory for scramblons in a single cBSYK model, which gives closed-form expressions for the late-time OTOC and operator size. In particular, the result for OTOC is consistent with numerical observations in [1]. We then study the entanglement dynamics in cBSYK chains. We derive the density dependence of the entanglement velocity for both Rényi entropies and the Von Neumann entropy, with a comparison to the butterfly velocity. We further consider adding repeated measurements and derive the effective theory of the measurement induced transition which shows U(2)L ⊗ U(2)R symmetry for non-interacting models.
Information scrambling is a hallmark of quantum chaos and thermalization in isolated quantum many-body systems. We investigate scrambling dynamics in the all-to-all interacting spin Sachdev-Ye-Kitaev (SYK)-qqq model using both pure- and mixed-state entanglement measures. We show that von-Neumann and Rényi entropies exhibit rapid growth followed by saturation near Haar-random values, signaling efficient scrambling. The scrambling rate reveals a nontrivial dependence on the interaction order, system size, and Hamiltonian scaling. We further employ mixed-state entanglement as a powerful probe of information scrambling. We numerically find a universal relation between the Rényi-1/2 mutual information and entanglement negativity for minimal interaction order in the early growth regime. Furthermore, entanglement negativity displays a Page-curve-like behavior under unequal subsystem partitioning, characterized by the birth, spread, and eventual death of quantum correlations. Our results provide a generic description of information scrambling using entanglement dynamics in all-to-all interacting spin systems with multi-body interactions.
Quenched disorder slows down the scrambling of quantum information. Using a bottom-up approach, we formulate a kinetic theory of scrambling in a correlated metal near a superconducting transition, following the scrambling dynamics as the impurity scattering rate is increased. Within this framework, we rigorously show that the butterfly velocity vvv is bounded by the light-cone velocity vlc{v}_{\mathrm{lc}}vlc​ set by the Fermi velocity. We analytically identify a disorder-driven dynamical transition occurring at small but finite disorder strength between a spreading of information characterized at late times by a discontinuous shock wave propagating at the maximum velocity vlc{v}_{\mathrm{lc}}vlc​, and a smooth traveling wave belonging to the Fisher or Kolmogorov-Petrovsky-Piskunov (FKPP) class and propagating at a slower, if not considerably slower, velocity vvv. In the diffusive regime, we establish the relation ${v}^{2}/{\ensuremath{\lambda}}_{\mathrm{FKPP}}\ensuremath{\sim}{D}_{\mathrm{el}}$, where ${\ensuremath{\lambda}}_{\mathrm{FKPP}}$ is the Lyapunov exponent set by the inelastic scattering rate and Del{D}_{\mathrm{el}}Del​ is the elastic diffusion constant.
We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of information spreading in generic dimensions. Their solutions show that scrambling propagates at the maximal speed set by the Fermi velocity. At early times, we find exponential growth at a rate set by the inelastic scattering. At late times, we find that scrambling is governed by shock-wave dynamics with traveling waves exhibiting a discontinuity at the boundary of the light cone. Notably, we find perfectly causal dynamics where the solutions do not spill outside of the light cone.