Abstract In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry—an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit long-lived signatures of both phase and frequency-locking.
Abstract In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry—an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit long-lived signatures of both phase and frequency-locking.
We present a concise review and perspective on noise-induced synchronisation and coherence protection in open quantum systems, with emphasis on recent work involving coupled spins, oscillators, and anyons. When local environments exhibit internal correlations, the structure of the noise determines which collective modes become decoherence-protected. This leads to steady-state entanglement, phase locking, and exceptional points (EPs) in the Liouvillian spectrum, signalling a collapse of the mode basis and the emergence of non-dissipative stabilised dynamics. Using a Lindblad framework, we show that symmetry in the noise correlations acts as a control parameter–protecting symmetric or antisymmetric modes depending on the sign of the correlation. In the pure-dephasing limit, coherence decay mirrors the Anderson–Kubo model, where the effective fluctuation strength scales as σ2(1±ξ), and the dynamical regime (Gaussian vs. Lorentzian) is set by the ratio σ/γ. Thus, the environment not only drives decoherence but can also selectively suppress it through symmetry filtering. We also revisit historical and conceptual origins of this idea, beginning with Huygens' synchronised pendulum clocks and culminating in modern non-Hermitian dynamics. Correlated noise–though classically stochastic–can organise quantum dynamics and protect coherence without direct control over the system. These insights offer a unifying view of synchronisation in classical and quantum regimes, with implications for quantum sensing, engineered decoherence, and long-lived coherence in complex environments such as biological light-harvesting complexes or avian magnetoreception.
We present a concise review and perspective on noise-induced synchronization and coherence protection in open quantum systems, with emphasis on recent work involving coupled spins, oscillators, and anyons. When local environments exhibit internal correlations, the structure of the noise determines which collective modes become decoherence-protected. This leads to steady-state entanglement, phase locking, and exceptional points (EPs) in the Liouvillian spectrum, signaling a collapse of the mode basis and the emergence of non-dissipative stabilized dynamics. Using a Lindblad framework, we show that symmetry in the noise correlations acts as a control parameter, protecting symmetric or antisymmetric modes depending on the sign of the correlation. In the pure-dephasing limit, coherence decay mirrors the Anderson-Kubo model, where the effective fluctuation strength scales as σ2(1±ξ), and the dynamical regime (Gaussian vs. Lorentzian) is set by the ratio σ/γ. Thus, the environment not only drives decoherence but can also selectively suppress it through symmetry filtering. We also revisit historical and conceptual origins of this idea, beginning with Huygens synchronized pendulum clocks and culminating in modern non-Hermitian dynamics. Correlated noise-though classically stochastic-can organize quantum dynamics and protect coherence without direct control over the system. These insights offer a unifying view of synchronization in classical and quantum regimes, with implications for quantum sensing, engineered decoherence, and long-lived coherence in complex environments such as biological light-harvesting complexes or avian magnetoreception.
Recently, several studies involving open quantum systems which possess a strong symmetry have observed that every individual trajectory in the Monte Carlo unravelling of the master equation will dynamically select a specific symmetry sector to ‘freeze’ into in the long-time limit. This phenomenon has been termed ‘dissipative freezing’, and in this paper we argue, by presenting several simple mathematical perspectives on the problem, that it is a general consequence of the presence of a strong symmetry in an open system with only a few exceptions. Using a number of example systems we illustrate these arguments, uncovering an explicit relationship between the spectral properties of the Liouvillian in off-diagonal symmetry sectors and the time it takes for freezing to occur. In the limiting case that eigenmodes with purely imaginary eigenvalues are manifest in these sectors, freezing fails to occur. Such modes indicate the preservation of information and coherences between symmetry sectors of the system and can lead to phenomena such as non-stationarity and synchronisation. The absence of freezing at the level of a single quantum trajectory provides a simple, computationally efficient way of identifying these traceless modes.
Abstract Real-world complex systems often show robust, persistent oscillatory dynamics, e.g.~non-trivial attractors. On the quantum level this behaviour has only been found in semi-classical or weakly correlated systems under restrictive assumptions. However, strongly interacting systems without classical limits, e.g.~electrons on a lattice or spins, typically relax quickly to a stationary state (trivial attractors). This raises the puzzling question of how non-trivial attractors can arise from the quantum laws. Here, we introduce strictly local dynamical symmetries that lead to extremely robust and persistent oscillations in quantum many-body systems without a classical limit. Observables that do not have overlap with the symmetry operators can relax, losing memory of their initial conditions. The remaining observables enter complex dynamical cycles, signalling the emergence of a quantum many-body attractor. We provide a recipe for constructing Hamiltonians featuring local dynamical symmetries. As an example, we introduce the spin lace – a model of a quasi-1D quantum magnet.
Strongly interacting quantum many-body systems are expected to thermalize, however, some evade thermalization due to symmetries. Quantum synchronization provides one such example of ergodicity breaking, but previous studies have focused on open systems. Here, motivated by the problem of ergodicity breaking in closed systems and the study of non-trivial dynamics, we investigate synchronization in a closed disordered Heisenberg spin chain. In the presence of large random disorder, strongly breaking the permutation symmetry of the system, we observe the emergence of spatial synchronization, where spins lock into locally synchronized patches. This behavior can be interpreted as a fragmentation of the global dynamical symmetry S+ into a collection of local dynamical symmetries, each characterized by a distinct frequency. In the weak-disorder regime, still without permutation symmetry, we show that the synchronization mechanism can be understood perturbatively within Krylov space. In the absence of disorder, the Krylov space associated with the dynamical symmetry S+ is two-dimensional. Introducing disorder couples this subspace to the remainder of the Krylov space. This coupling leads only to a second-order correction to the frequency of the dynamical symmetry, thereby preserving coherent oscillations despite the presence of small disorder. At stronger disorder, the perturbation modifies S+ so that it acquires a finite lifetime, providing an example of a transient dynamical symmetry.
Spontaneous synchronization between coupled periodic systems occur in a wealth of classical physical setups. Here, we show theoretically that the phase of two distinct quantum harmonic oscillators spontaneously synchronize when they are strongly coupled to a common bosonic quantum dissipative environment at zero temperature, in the absence of any driving mechanism. To do so, we compute the dynamics of the oscillators with an exact master equation obtained from a path integral formalism. Above some value of the system-environment coupling strength, we observe numerically a strongly reduced damping and a frequency locking in the dynamics of the oscillators. Beyond the synchronization mechanism, we also describe the rich phenomenology of the dynamics in the model and notably identify the additional emergence of a regime with long-lived oscillations.