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.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.

cond-mat.dis-nnCross-listedarXiv:2602.11431Feb 13, 20260 citations

Discrete Time Crystals in the Absence of Manifest Symmetries or Disorder in Open Quantum Systems

Filippo Maria Gambetta, Federico Carollo, Matteo Marcuzzi +2 more

We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of disorder, but relies instead on the emergence of a metastable regime. We investigate this in detail in an open quantum spin system, which is a canonical model for the exploration of collective phenomena in strongly interacting dissipative Rydberg gases. Here, a semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role. We perform numerical simulations in order to investigate the dependence on the range of interactions, from all to all to short ranged, and the scaling with system size of the lifetime of the time crystal.We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of disorder, but relies instead on the emergence of a metastable regime. We investigate this in detail in an open quantum spin system, which is a canonical model for the exploration of collective phenomena in strongly interacting dissipative Rydberg gases. Here, a semiclassical approach reveals the emergence of a robust discrete time-crystalline phase in the thermodynamic limit in which metastability, dissipation, and interparticle interactions play a crucial role. We perform numerical simulations in order to investigate the dependence on the range of interactions, from all to all to short ranged, and the scaling with system size of the lifetime of the time crystal.

arXiv:1807.10161Physical Review LettersJan 8, 2019149 citations

Dynamical Localization in Disordered Quantum Spin Systems

Eman Hamza, Robert Sims, Günter Stolz

arXiv:1108.3811Communications in Mathematical PhysicsAug 1, 201287 citations

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.