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Abstract. Many-body problems have seen a remarkable resurgence in recent years. In part, this is because 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. Among these, quantum small-worlds are quantum many-body systems that interpolate between completely ordered (nearest-neighbour, next-to-nearest-neighbour etc.) and completely random interactions. As such, they furnish a novel new laboratory to study quantum systems transitioning between regular and chaotic behaviour. In this talk, 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 these ideas can be related to models of viral spreading in real-world systems.
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