Field theory for monitored Brownian SYK clusters

• URL: http://arxiv.org/abs/2410.08079v2
• Date: Mon, 4 Nov 2024 13:45:05 GMT
• Title: Field theory for monitored Brownian SYK clusters
• Authors: Anastasiia Tiutiakina, Hugo Lóio, Guido Giachetti, Jacopo De Nardis, Andrea De Luca,
• Abstract summary: We consider the time evolution of multiple clusters of Brownian Sachdev-Ye-Kitaev systems. We construct a coherent states path integral of the dynamics by generalizing spin coherent states for higher symmetry groups. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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