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arXiv · 2404.10919

Tensor product random matrix theory

Alexander Altland·Joaquim Telles de Miranda·Tobias Micklitz
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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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Alexander Altland, Joaquim Telles de Miranda, Tobias Micklitz. 2024-04-16. Tensor product random matrix theory. https://doi.org/10.1103/physrevresearch.6.l042029

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