Scrambling and Chaos in Quantum Networks

Many-body problems have seen a remarkable resurgence in recent years. In part, this is because of the increasing overlap between high energy particle physics and theoretical condensed matter. The discovery of the SYK model and the avalanche of work that followed is testament to this state of affairs. Network theory (or graph theory) offers a powerful toolkit to study some of these systems in a relatively model-independent and computationally efficient way. As such, they furnish a novel new laboratory to study quantum systems exhibiting a number of remarkable features such as transitioning between regular and chaotic behaviour. In this colloquium, I will introduce these ideas and illustrate them in the context of the Heisenberg and Ising models, showing how to inject a small number of long-range interactions into the spin chain and study its ability to scramble quantum information using two primary devices: the out-of-time-order correlator (OTOC) and the spectral form factor (SFF). As an interesting, and perhaps timely, aside I will describe how (the classical version of) these ideas can be related to models of viral spreading and vaccine distribution in real-world systems.

Zoom link available upon request at physics@wustl.edu.