Super-Logarithmic Entanglement Scaling in a Monitored Superconducting Chain

Abstract:We study the entanglement dynamics of a one-dimensional spinful $s$-wave superconductor subjected to local continuous measurements. In the rare-measurement regime, we derive a replicated Keldysh non-linear sigma model (NLSM) to describe the steady-state entanglement. Within this field-theoretic framework, the interplay between measurement dephasing and superconducting pairing constrains the low-energy, long-wavelength fluctuations to an $\mathrm{SO(R)}$ target manifold. A one-loop renormalization-group analysis shows that the theory develops a weak-anti-localization flow, stabilizing a critical phase with super-logarithmic scaling of the steady-state entanglement. Our field-theoretic results explain the numerical evidence reported in the companion Letter [arXiv:2604.04375] and demonstrate that such a critical phase can emerge in a one-dimensional topologically trivial superconductor without relying on topological protection.

26 pages, companion paper to arXiv:2604.04375, no figure. Comments are welcome

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Superconductivity (cond-mat.supr-con)

arXiv:2607.07835 [quant-ph]

(or arXiv:2607.07835v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.07835 Focus to learn more arXiv-issued DOI via DataCite

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