Tensor product random matrix theory
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910678655172608 |
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| author | Altland, Alexander de Miranda, Joaquim Telles Micklitz, Tobias |
| author_facet | Altland, Alexander de Miranda, Joaquim Telles Micklitz, Tobias |
| contents | 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 $G Σ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10919 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor product random matrix theory Altland, Alexander de Miranda, Joaquim Telles Micklitz, Tobias Mesoscale and Nanoscale Physics Quantum Physics 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 $G Σ$-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. |
| title | Tensor product random matrix theory |
| topic | Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2404.10919 |