2020/02/29 by Bryce Kobrin, Zhenbin Yang, Gregory D. Kahanamoku-Meyer +4 · 2 citations
Physics and Astronomy · #cond-mat.quant-gas #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevlett.126.030602
published as Phys. Rev. Lett. 126, 030602 (2021) · 6+15 pages, 3+11 figures. v3 published version, with corrected prefactor in Eq. 1
arxiv created 2021/04/06 · arxiv updated 2021/04/08
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, λ, across a wide range in temperatures, including in the regime where λ approaches the universal bound, λ= 2π/β.