Many-Body Chaos in the Sachdev-Ye-Kitaev Model

• URL: http://arxiv.org/abs/2002.05725v3
• Date: Tue, 6 Apr 2021 22:33:46 GMT
• Title: Many-Body Chaos in the Sachdev-Ye-Kitaev Model
• Authors: Bryce Kobrin, Zhenbin Yang, Gregory D. Kahanamoku-Meyer, Christopher T. Olund, Joel E. Moore, Douglas Stanford, and Norman Y. Yao
• Abstract summary: Many-body chaos is a powerful framework for understanding thermalization in strongly interacting quantum systems. We develop a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators. We verify that this procedure accurately determines the Lyapunov exponent, $lambda$, across a wide range in temperatures.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. While recent analytic advances have sharpened our intuition for many-body chaos in certain large $N$ theories, it has proven challenging to develop precise numerical tools capable of exploring this phenomenon in generic Hamiltonians. To this end, we utilize massively parallel, matrix-free Krylov subspace methods to calculate dynamical correlators in the Sachdev-Ye-Kitaev (SYK) model for up to $N = 60$ Majorana fermions. We begin by showing that numerical results for two-point correlation functions agree at high temperatures with dynamical mean field solutions, while at low temperatures finite-size corrections are quantitatively reproduced by the exactly solvable dynamics of near extremal black holes. Motivated by these results, we develop a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators (OTOCs). We verify that this procedure accurately determines the Lyapunov exponent, $\lambda$, across a wide range in temperatures, including in the regime where $\lambda$ approaches the universal bound, $\lambda = 2\pi/\beta$.

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