A self-organizing map fed with raw Hamiltonian matrices responds along the same rewiring-probability axis where spectral r-ratios show a Poisson-to-GUE crossover, though the response may reflect graph geometry instead of chaos.
Chaos and Scrambling in Quantum Small Worlds
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abstract
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 article, we introduce the idea of a quantum small-world network by starting from a well understood integrable system, a spin-1 Heisenberg chain. We then 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). We find that the system shows increasingly rapid scrambling as its interactions become progressively more random, with no evidence of quantum chaos.
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Unsupervised Techniques to Detect Quantum Chaos
A self-organizing map fed with raw Hamiltonian matrices responds along the same rewiring-probability axis where spectral r-ratios show a Poisson-to-GUE crossover, though the response may reflect graph geometry instead of chaos.