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.
Tensor product random matrix theory
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abstract
The evolution of complex correlated quantum systems such as random circuit networks is governed by the dynamical buildup of both entanglement and entropy. We here introduce a real-time field theory approach -- essentially a fusion of the $G \Sigma$-functional of the SYK-model and the field theory of disordered systems -- enigneered to microscopically describe the full range of such crossover dynamics: from initial product states to a maximum entropy ergodic state. To showcase this approach in the simplest nontrivial setting, we consider a tensor product of coupled random matrices, and compare to exact diagonalization.
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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.