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

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 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. Our procedure accurately determines the Lyapunov exponent, lambda, across a wide range in temperatures, including in the regime where. approaches the universal bound, lambda = 2 pi/beta.

Automated summary

Researchers have utilized massively parallel, matrix-free Krylov subspace methods to study dynamical correlators in the Sachdev-Ye-Kitaev model, finding agreement with dynamical mean field solutions at high temperatures and accurate reproduction of finite-size corrections at low temperatures using the dynamics of near extremal black holes. They have also developed a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators and accurately determining the Lyapunov exponent across a wide range of temperatures.