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arXiv:2510.11450 · Physical review. E

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

David Soldner, Igor Lesanovsky, Gabriele Perfetto

Published May 27, 2026• 1 citation
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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.

DOI
10.1103/lnt2-k8g3

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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.
We investigate the dynamics of a noninteracting spin system, undergoing coherent Rabi oscillations, in the presence of stochastic resetting. We show that resetting generally induces long-range quantum and classical correlations both in the emergent dissipative dynamics and in the nonequilibrium stationary state. Moreover, for the case of conditional reset protocols---where the system is reinitialized to a state dependent on the outcome of a preceding measurement---we show that in the thermodynamic limit, the spin system can feature collective behavior which results in a phenomenology reminiscent of that occurring in nonequilibrium phase transitions. The discussed reset protocols can be implemented on quantum simulators and quantum devices that permit fast measurement and readout of macroscopic observables, such as the magnetization. Our approach does not require the control of coherent interactions and may therefore highlight a route towards a simple and robust creation of quantum correlations and collective nonequilibrium states, with potential applications in quantum enhanced metrology and sensing.
Stochastic resetting has emerged as a versatile protocol to drive quantum many-body systems to non-equilibrium steady states by interspersing unitary dynamics with measurements and resets at random times. In spite of this, a quantum hardware validation of such non-equilibrium steady states is still missing. Here, we achieve this goal by first formulating a noisy discrete-time theory where unitary gates alternate with noisy mid-circuit projective measurements and conditional resets. This noisy conditional resetting theory is then demonstrated on a superconducting quantum processor for up to N=7N=7N=7 qubits. We consider, as a paradigmatic case, the unitary dynamics of the interacting Floquet transverse-field Ising model. The stationary state of the noisy conditional resetting agrees quantitatively with the experiments, and it shows crossover behavior related to the equilibrium quantum phase transition of the model. Our results might thus pave the way for the preparation of collective stationary states on noisy quantum devices and for further developments of quantum algorithms involving mid-circuit measurements.
We consider closed quantum many-body systems subject to stochastic resetting. This means that their unitary time evolution is interrupted by resets at randomly selected times. When a reset takes place, the system is reinitialized to a state chosen from a set of reset states conditionally on the outcome of a measurement taken immediately before resetting. We construct analytically the resulting nonequilibrium stationary state, thereby establishing an explicit connection between quantum quenches in closed systems and the emergent open system dynamics induced by stochastic resetting. We discuss as an application the paradigmatic transverse-field quantum Ising chain. We show that signatures of its ground-state quantum phase transition are visible in the steady state of the reset dynamics as a sharp crossover. Our findings show that a controlled stochastic resetting dynamics allows one to design nonequilibrium stationary states of quantum many-body systems, where uncontrolled dissipation and heating can be prevented. These states can thus be created on demand and exploited, e.g., as a resource for quantum enhanced sensing on quantum simulator platforms.
Stochastic resetting describes dynamics which are reinitialized to a reference state at random times. These protocols are attracting significant interest: they can stabilize nonequilibrium stationary states, generate correlations in noninteracting systems, and enable optimal search strategies. While a constant reset probability results in a Markovian dynamics, much less is known about non-Markovian effects in quantum stochastic resetting. Here, we analyze memory effects in these processes -- examining the evolution of quantum states and of observables -- through witnesses of non-Markovianity for open quantum systems. We focus on discrete-time reset processes, which are of particular interest as they can be implemented on existing gate-operated quantum devices. We show that these processes are generically described by non-divisible maps and, in non-classical scenarios where the effective reset probability can become negative, can feature revivals in the state distinguishability. Our results reveal non-Markovian effects in quantum stochastic resetting and show that a time-dependent reset may be exploited to engineer enhanced stationary quantum correlations.
Speeding up the relaxation dynamics of many-body quantum systems is important in a variety of contexts, including quantum computation and state preparation. We demonstrate that such acceleration can be universally achieved via transient stochastic resetting. This means that during an initial time interval of finite duration, the dynamics is interrupted by resets that take the system to a designated state at randomly selected times. We illustrate this idea for few-body open systems and also for a challenging many-body case, where a first-order phase transition leads to a divergence of relaxation time. In all scenarios, a significant and sometimes even exponential acceleration in reaching the stationary state is observed, similar to the so-called Mpemba effect. The universal nature of this speedup lies in the fact that the design of the resetting protocol only requires knowledge of a few macroscopic properties of the target state, such as the order parameter of the phase transition, while it does not necessitate any fine-tuned manipulation of the initial state.
We study nonequilibrium dynamics of integrable and nonintegrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate rrr, that project the system to its initial state. We show that the steady-state density matrix of a nonintegrable system, averaged over the reset distribution, retains its off-diagonal elements for any finite rrr. Consequently a generic observable $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{O}$, whose expectation value receives a contribution from these off-diagonal elements, never thermalizes under such dynamics for any finite rrr. We demonstrate this phenomenon by exact numerical studies of experimentally realizable models of ultracold bosonic atoms in a tilted optical lattice. For integrable Dirac-like fermionic models driven periodically between such resets, the reset-averaged steady state is found to be described by a family of generalized Gibbs ensembles characterized by rrr. We also study the spread of particle density of a noninteracting one-dimensional fermionic chain, starting from an initial state where all fermions occupy the left half of the sample, while the right half is empty. When driven by resetting dynamics, the density profile approaches at long times to a nonequilibrium stationary profile that we compute exactly. We suggest concrete experiments that can possibly test our theory.