Tensor product random matrix theory
arXiv:2404.10919 · doi:10.1103/PhysRevResearch.6.L042029
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 -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.
6 pages, 3 figures
References in corpus (15)
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Solution of a minimal model for many-body quantum chaos
- Spectral statistics in spatially extended chaotic quantum many-body systems
- Entanglement Transitions from Holographic Random Tensor Networks
- Electron--electron Interactions in Disordered Metals: Keldysh Formalism
- An introduction to the SYK model
- Quantum ergodicity in the SYK model
- Local pairing of Feynman histories in many-body Floquet models
- Percolation in Fock space as a proxy for many-body localisation
- Entanglement and localization transitions in eigenstates of interacting chaotic systems
- Universal scaling of spectral fluctuation transitions for interacting chaotic systems
- Eigenstate entanglement between quantum chaotic subsystems: universal transitions and power laws in the entanglement spectrum
- Universal Dephasing Mechanism of Many-Body Quantum Chaos
- Entanglement in coupled kicked tops with chaotic dynamics
- Entanglement production by interaction quenches of quantum chaotic subsystems