Super-maximal chaos and instability

TL;DR

This paper explores the limits of chaos in quantum systems, proposing that exceeding the chaos bound causes instability, supported by findings in a SYK lattice model revealing novel phases and divergent transport properties at phase transitions.

Contribution

It introduces the idea that super-maximal chaos induces instability and demonstrates this through a SYK lattice model with tunable parameters.

Findings

Super-maximal chaos leads to system instability.

Discovery of a novel phase with unconventional transport properties.

Divergence of diffusion coefficient, butterfly velocity, and Thouless time at phase transition.

Abstract

An upper bound on Lyapunov exponent of a thermal many body quantum system has been conjectured recently. In this work, we attempt to achieve a physical understanding of what prevents a system from violating this bound. To this end, we propose - super-maximal chaos leads to instability. Our proposal is supported by findings in a SYK lattice model, with a tuneable parameter, which the Lyapunov spectrum depends upon. In the stable regime of this parameter, along with incoherent metallic phase, the system exhibits another novel phase, where transport is controlled neither by quasi-particles nor by diffusion. At the phase transition, diffusion coefficient, butterfly velocity and Thouless time diverges.