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 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, λ, across a wide range in temperatures, including in the regime where λ approaches the universal bound, λ=2π/β.
Highlights
Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems
Characterizing thermalization in strongly interacting quantum systems is a goal that spans across multiple disciplines ranging from condensed matter and quantum information to quantum gravity
Recent developments toward this goal have revealed striking insights into the relationship between quantum chaos and the delocalization, or scrambling, of quantum information. This unification is partly provided by the notion of out-of-time-order correlators (OTOCs), which take the general form hWðtÞVð0ÞWðtÞVð0Þi for local operators V and W [1,2,3]
Summary
Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. 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. We compute correlation functions for the SYK model for systems of up to N 1⁄4 60 Majorana fermions and leverage the model’s correspondence with quantum gravity to interpret finitesize effects.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
