Recent work has shown that a variety of novel phases of matter arise in periodically driven Floquet systems. Among these are many-body localized phases which spontaneously break global symmetries and exhibit novel multiplets of Floquet eigenstates separated by quantized quasienergies. Here we show that these properties are stable to all weak local deformations of the underlying Floquet drives---including those that explicitly break the defining symmetries---and that the models considered until now occupy submanifolds within these larger ``absolutely stable'' phases. While these absolutely stable phases have no explicit global symmetries, they spontaneously break Hamiltonian-dependent emergent symmetries, and thus continue to exhibit the novel multiplet structure. The multiplet structure in turn encodes characteristic oscillations of the emergent order parameter at multiples of the fundamental period. Altogether these phases exhibit a form of simultaneous long-range order in space and time which is new to quantum systems. We describe how this spatiotemporal order can be detected in experiments involving quenches from a broad class of initial states.
Recent work has shown that a variety of novel phases of matter arise in periodically driven Floquet systems. Among these are many-body localized phases which spontaneously break global symmetries and exhibit novel multiplets of Floquet eigenstates separated by quantized quasienergies. Here we show that these properties are stable to all weak local deformations of the underlying Floquet drives---including those that explicitly break the defining symmetries---and that the models considered until now occupy submanifolds within these larger ``absolutely stable'' phases. While these absolutely stable phases have no explicit global symmetries, they spontaneously break Hamiltonian-dependent emergent symmetries, and thus continue to exhibit the novel multiplet structure. The multiplet structure in turn encodes characteristic oscillations of the emergent order parameter at multiples of the fundamental period. Altogether these phases exhibit a form of simultaneous long-range order in space and time which is new to quantum systems. We describe how this spatiotemporal order can be detected in experiments involving quenches from a broad class of initial states.
Recent work has shown that a variety of driven phases of matter arise in Floquet systems. Among these are many-body localized phases which spontaneously break unitary symmetries and exhibit novel multiplets of Floquet eigenstates separated by quantized quasienergies. Here we show that these properties are to {\it all} weak local deformations of the underlying Floquet drives, and that the models considered until now occupy sub-manifolds within these larger stable phases. While these absolutely phases have no explicit Hamiltonian independent global symmetries, they spontaneously break Hamiltonian dependent {\it emergent} unitary or anti-unitary symmetries, and thus continue to exhibit the novel multiplet structure. We show that the out of equilibrium dynamics exhibit a lack of synchrony with the drive characterized by infinitely many distinct frequencies, most incommensurate with the fundamental period --- i.e., these phases look like time glasses. Floquet eigenstates, however, exhibit a purely commensurate temporal crystalline periodicity for a special class of bilocal operators with infinite separation which reflects the dynamics of the order parameter for the emergent symmetries.
A periodically driven quantum many-body system is believed to approach a locally infinite-temperature-like state as dictated by the ergodicity hypothesis, when all the couplings/parameters are of the same order. When the drive is stronger than a threshold value, a large class of systems is shown to break this mandate, exhibiting Dynamical Freezing (DF): ergodicity is broken due to the emergence of local operators with permanent memory of their initial values (PRX 11, 021008, 2021). However, an exception to DF has recently been noted in a particular setting (PRX 16, 011041, 2026). Here we identify the condition for ergodicity-breaking in a system under strong drive, and show how to stabilize DF by exact, local engineering. We further show that the Floquet Hamiltonian Heff=(i/T)ln[U(T)] is non-local when ordered by spin-flips, in a non-DF system, while it turns quasi-local under our simple, local DF engineering that keeps the Hamiltonian H(t) still non-integrable at each t. This perplexing non-universality is absent in equilibrium, where non-integrability is believed to imply ergodicity and thermalization universally. Our work paves a way to engineering novel ergodicity-broken interacting Floquet phases of matter in various quantum platforms, and also endows DF-assisted quantum error mitigation and state stabilization techniques (see Nature 653, 1027 (2026)) with unprecedented versatility and flexibility.
Phases of matter are traditionally seen as families of static systems exhibiting the same long-distance and low-energy correlations. In this work, the authors propose and classify a new family of phases of matter. They are novel insofar as they are intrinsically driven and out of equilibrium --- they can only be realized in systems with time-dependent Hamiltonians. The phases we consider arise in 1D periodically driven systems, in the presence of strong disorder and interactions, and are similar to but qualitatively distinct from the symmetry-protected topological phases now well known in the equilibrium setting. In a companion paper, the authors examine similar intrinsically driven families of states with long-range order, and an order parameter that oscillates at a frequency that is robustly an integer multiple of the underlying drive frequency.
We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics of ensembles of classical trajectories despite the breakdown of this description at the single trajectory level. In addition, we prove that the effective Hamiltonian can host emergent symmetries protected by the discrete time-translation symmetry of the drive. The spontaneous breaking of such an emergent symmetry leads to a subharmonic response, characteristic of time crystalline order, that survives to exponentially late times in the frequency of the drive. To this end, we numerically demonstrate the existence of classical prethermal time crystals in systems with different dimensionalities and ranges of interaction. Extensions to higher order and fractional time crystals are also discussed.
We propose the concept of a spontaneous many-body Floquet state. This is a state that, in the absence of external periodic driving, self-oscillates like in the presence of a periodic Hamiltonian, this behavior being spontaneously induced by many-body interactions. In addition, its quantum fluctuations are described by regular Floquet theory. Furthermore, it is also a time crystal, presenting long-range time-periodic order. However, this crystalline behavior is very different to that of conventional Floquet discrete time crystals: here, there is no external periodic driving, energy is conserved, and the nature of the spontaneous symmetry breaking is continuous instead of discrete. We demonstrate that spontaneous many-body Floquet states can emerge in a variety of canonical many-body problems, ranging from interacting fermions to Bose-Hubbard models. We specifically show that a spontaneous many-body Floquet state is a universal intrinsic state of a one-dimensional flowing atom condensate, both subsonic and supersonic, resulting from a dynamical phase transition and robust against external perturbations and quantum fluctuations, proposing also realistic experimental scenarios for its observation. A spontaneous many-body Floquet state not only represents a realization of a continuous time crystal, but also another paradigm in Floquet physics.
Many-body localization (MBL) lends remarkable robustness to nonequilibrium phases of matter. Such phases can show topological and symmetry-breaking order in their ground and excited states, but they may also belong to an anomalous localized topological phase (ALT phase). All eigenstates in an ALT phase are trivial, in that they can be deformed to product states, but the entire Hamiltonian cannot be deformed to a trivial localized model without going through a delocalization transition. Using a correspondence between MBL phases with short-ranged entanglement and locality-preserving unitaries, called quantum cellular automata (QCA), we reduce the classification of ALT phases to that of QCA. This method extends to periodically (Floquet) and quasiperiodically driven ALT phases, and captures anomalous Floquet phases within the same framework as static phases. We considerably develop the study of the topology of QCA, allowing us to classify static and driven ALT phases in low dimensions. The QCA framework further generalizes to include symmetry-enriched ALT phases (SALT phases), which we also classify in low dimensions, and provides a large class of soluble models suitable for realization in quantum simulators. In systematizing the study of ALT phases, we both greatly extend the classification of interacting nonequilibrium systems and clarify a confusion in the literature which implicitly equates nontrivial Hamiltonians with nontrivial ground states.