Tensor product random matrix theory

• URL: http://arxiv.org/abs/2404.10919v2
• Date: Wed, 30 Oct 2024 18:29:00 GMT
• Title: Tensor product random matrix theory
• Authors: Alexander Altland, Joaquim Telles de Miranda, Tobias Micklitz,
• Abstract summary: We introduce a real-time field theory approach to the evolution of correlated quantum systems. We describe the full range of such crossover dynamics, from initial product states to a maximum entropy ergodic state.
• Score: 39.58317527488534
• License:
• 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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