Field theory for monitored Brownian SYK clusters
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912483755687936 |
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| author | Tiutiakina, Anastasiia Lóio, Hugo Giachetti, Guido De Nardis, Jacopo De Luca, Andrea |
| author_facet | Tiutiakina, Anastasiia Lóio, Hugo Giachetti, Guido De Nardis, Jacopo De Luca, Andrea |
| contents | We consider the time evolution of multiple clusters of Brownian Sachdev-Ye-Kitaev (SYK), i.e. systems of N Majorana fermions with a noisy interaction term. In addition to the unitary evolution, we introduce two-fermion monitorings. We construct a coherent states path integral of the dynamics by generalizing spin coherent states for higher symmetry groups. We then demonstrate that the evolution of the replicated density matrix can be described by an effective field theory for the "light" degrees of freedom, i.e. the quantum fluctuations generated by the unitary evolution. This method is applied to both quadratic, where the field theory reduces to the nonlinear sigma model (NLSM), and also to interacting SYK clusters. We show that in the stationary regime, two monitored clusters exhibit linear-in-N entanglement, with a proportionality factor dependent on the strength of the unitary coupling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08079 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Field theory for monitored Brownian SYK clusters Tiutiakina, Anastasiia Lóio, Hugo Giachetti, Guido De Nardis, Jacopo De Luca, Andrea Statistical Mechanics Disordered Systems and Neural Networks Quantum Physics We consider the time evolution of multiple clusters of Brownian Sachdev-Ye-Kitaev (SYK), i.e. systems of N Majorana fermions with a noisy interaction term. In addition to the unitary evolution, we introduce two-fermion monitorings. We construct a coherent states path integral of the dynamics by generalizing spin coherent states for higher symmetry groups. We then demonstrate that the evolution of the replicated density matrix can be described by an effective field theory for the "light" degrees of freedom, i.e. the quantum fluctuations generated by the unitary evolution. This method is applied to both quadratic, where the field theory reduces to the nonlinear sigma model (NLSM), and also to interacting SYK clusters. We show that in the stationary regime, two monitored clusters exhibit linear-in-N entanglement, with a proportionality factor dependent on the strength of the unitary coupling. |
| title | Field theory for monitored Brownian SYK clusters |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Quantum Physics |
| url | https://arxiv.org/abs/2410.08079 |