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Tensor product random matrix theory
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DOI：10.1103/PhysRevResearch.6.L042029.png)
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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 E functional of the SYK model and the field theory of disordered systems-engineered 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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