Chaos in deformed SYK models

Abstract

The SYK model has attracted significant interest for its maximal chaos, connections to two-dimensional holography, and relevance to strange metals. Two signatures of chaos in this model are out-of-time-ordered correlators (OTOCs) and Krylov complexity, both exhibiting early-time exponential behaviours characterized by the Lyapunov and Krylov exponents, respectively. In this talk, I explore these quantities in a class of relevant deformations of the SYK model, including flows which interpolate between two regions of near-maximal chaos and flows that lead to a nearly-integrable behaviour at low temperatures. I present both analytic and numerical results showing that the Krylov exponent consistently upper-bounds the Lyapunov exponent. Notably, while the Lyapunov exponent varies non-monotonically with temperature, the Krylov exponent remains smooth and monotonic, showing no clear signatures across chaotic transitions. This challenges the effectiveness of Krylov complexity as a diagnostic of chaos in quantum mechanical systems. I will also comment on the potential relevance of SYK flows for de Sitter holography and on connections to other recent works.