Tensor product random matrix theory
- URL: http://arxiv.org/abs/2404.10919v1
- Date: Tue, 16 Apr 2024 21:40:57 GMT
- Title: Tensor product random matrix theory
- Authors: Alexander Altland, Tobias Micklitz, Joaquim Telles de Miranda,
- 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: http://creativecommons.org/licenses/by/4.0/
- 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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