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Nonanaliticities and ergodicity breaking in noninteracting many-body dynamics via stochastic resetting and global measurements

David Soldner1,*, Igor Lesanovsky2,3, and Gabriele Perfetto4,†

  • 1Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
  • 2Institut für Theoretische Physik and Center for Integrated Quantum Science and Technology, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
  • 3School of Physics and Astronomy and Center for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, Nottingham NG7 2RD, United Kingdom
  • 4Institut für Theoretische Physik, ETH Zürich, Wolfgang-Pauli-Str. 27, 8093 Zürich, Switzerland

  • *Contact author: david.soldner@student.uni-tuebingen.de
  • †Contact author: gperfetto@phys.ethz.ch
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Phys. Rev. E 114, 014105 – Published 6 July, 2026

DOI: https://doi.org/10.1103/lnt2-k8g3

Abstract

Stochastic resetting generates nonequilibrium steady states by interspersing unitary quantum dynamics with resets at random times. When the state to which the system is reset is chosen conditionally on the outcome of a global and spatially resolved measurement, the steady state can feature collective behavior similar to what is typically observed at phase transitions. Here we investigate such conditional reset protocol in a system of noninteracting spins, where the reset state is chosen as a magnetization eigenstate, that is selected (conditioned) on the outcome of a previous magnetization measurement. The stationary states that emerge from this protocol are characterized by the density of spins in a given magnetization eigenstate, which is the analog of the order parameter. The resulting stationary phase diagram features multiple nonanalytic points. They are of first-order type for half-integer spin, while multicritical behavior, signalled by both first and second-order discontinuities, is found for integer spin. We also show that the associated dynamics is nonergodic, i.e., which stationary state the system ultimately assumes is determined by the initial state. Interestingly, the mechanism underlying these phenomena does not rely on interactions, but the emergent nonlinear behavior is solely a consequence of correlations induced by the measurement.

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Phys. Rev. E 114, 014105– Published 6 July, 2026
  • Received 23 October 2025
  • Accepted 27 May 2026
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