Field theory for monitored Brownian SYK clusters

Anastasiia Tiutiakina; Hugo Lóio; Guido Giachetti; Jacopo De Nardis; Andrea De Luca

doi:10.22331/q-2025-07-14-1794

Field theory for monitored Brownian SYK clusters

Anastasiia Tiutiakina, Hugo Lóio, Guido Giachetti, Jacopo De Nardis, and Andrea De Luca

Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université, 95302 Cergy-Pontoise Cedex, France

Published:	2025-07-14, volume 9, page 1794
Editor:	Carlo Beenakker
Eprint:	arXiv:2410.08079v3
Doi:	https://doi.org/10.22331/q-2025-07-14-1794
Citation:	Quantum 9, 1794 (2025).

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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.

Popular summary

Recently, physicists have begun exploring how continuously measuring quantum systems affects their entanglement. Frequent measurements tend to disrupt quantum correlation, while gentler measurements allow quantum information to “scramble”. Meanwhile, measurement-induced phenomena arise when repeated observations significantly alter the quantum state of a system. This interplay between evolution and measurement leads to novel quantum phases that are challenging to analyze, requiring theoretical approaches and approximations, such as field theory.
In our paper, “Field theory for monitored Brownian SYK clusters,” we study a system of fermions evolving under measurements and unitary evolution. We choose the celebrated Sachdev–Ye–Kitaev (SYK) model—as a simple example of a quantum system where particles interact strongly and quickly scramble quantum information. Interestingly, the SYK model has gained attention because it shares similarities with black hole physics, offering insights into complex phenomena like entropy, information scrambling, and quantum information paradoxes.
We developed a theoretical approach called a field theory to accurately describe the behavior of particle clusters under continuous monitoring. Using coherent states, we derived a practical mathematical model known as a non-linear sigma model that has been extensively studied in the last 60 years, and provides insights into the phases of matter occurring in the monitored systems.
Our findings help to deepen our understanding of quantum chaos, entanglement, and the intriguing effects of measurement, potentially guiding the development of future quantum technologies, including quantum computing and secure quantum communication.

► BibTeX data

@article{Tiutiakina2025fieldtheory,
  doi = {10.22331/q-2025-07-14-1794},
  url = {https://doi.org/10.22331/q-2025-07-14-1794},
  title = {Field theory for monitored {B}rownian {SYK} clusters},
  author = {Tiutiakina, Anastasiia and L{\'{o}}io, Hugo and Giachetti, Guido and Nardis, Jacopo De and Luca, Andrea De},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1794},
  month = jul,
  year = {2025}
}

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[5] Philippe Lecheminant, Yuya Tanizaki, and Keisuke Totsuka, "Infrared properties of two-dimensional SU(N)/H nonlinear \sigma models at nonzero \theta angles", SciPost Physics 18 6, 183 (2025).

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