We prove the existence of non-equilibrium phases of matter in the prethermal regime of periodically-driven, long-range interacting systems, with power-law exponent $α> d$, where $d$ is the dimensionality of the system. In this context, we predict the existence of a disorder-free, prethermal discrete time crystal in one dimension -- a phase strictly forbidden in the absence of long-range interactions. Finally, using a combination of analytic and numerical methods, we highlight key experimentally observable differences between such a prethermal time crystal and its many-body localized counterpart.
Nonequilibrium dynamics of an isolated quantum spin chain with long-range Ising interactions that decay as $1/r^α$ ($0<α<1$) with the distance $r$ is studied. It turns out that long-range interactions give rise to a big timescale separation, which causes prethermalization for all $α\in(0,1)$. This conclusion is deduced by comparing two important timescales relevant for relaxation dynamics; one is the relaxation time of local permutation operators, which are quasi-conserved quantities in this system, and the other is the timescale of the initial relaxation due to the growth of quantum fluctuati…
It is by now well established that periodically driven quantum many-body systems can realize topological nonequilibrium phases without any equilibrium counterpart. Here we show that, even in the absence of time translation symmetry, nonequilibrium topological phases of matter can exist in aperiodically driven systems for tunably parametrically long prethermal lifetimes. As a prerequisite, we first demonstrate the existence of longlived prethermal Anderson localization in two dimensions under random multipolar driving. We then show that the localization may be topologically nontrivial with a qu…
Systems subject to a high-frequency drive can spend an exponentially long time in a prethermal regime, in which novel phases of matter with no equilibrium counterpart can be realized. Due to the notorious computational challenges of quantum many-body systems, numerical investigations in this direction have remained limited to one spatial dimension, in which long-range interactions have been proven a necessity. Here, we show that prethermal non-equilibrium phases of matter are not restricted to the quantum domain. Studying the Hamiltonian dynamics of a large three-dimensional lattice of classic…
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, characteristi…
In periodically-driven quantum systems, resonances can induce exotic nonequilibrium behavior and new phases of matter without static analog. We report on the emergence of fractional and integer resonances in a broad class of many-body Hamiltonians with a modulated hopping with a frequency that is either a fraction or an integer of the on-site interaction. We contend that there is a fundamental difference between these resonances when interactions bring the system to a Floquet prethermal state. Second-order processes dominate the dynamics in the fractional resonance case, leading to less entang…
The use of periodic driving for synthesizing many-body quantum states depends crucially on the existence of a prethermal regime, which exhibits drive-tunable properties while forestalling the effects of heating. This motivates the search for direct experimental probes of the underlying localized nonergodic nature of the wave function in this metastable regime. We report experiments on a many-body Floquet system consisting of atoms in an optical lattice subjected to ultrastrong sign-changing amplitude modulation. Using a double-quench protocol we measure an inverse participation ratio quantifyi…
We provide a comprehensive account of prethermal discrete time crystals within classical Hamiltonian dynamics, complementing and extending our recent work [Phys. Rev. Lett. 127, 140602 (2021)]. Considering power-law interacting spins on one-, two-, and three-dimensional hypercubic lattices, we investigate the interplay between dimensionality and interaction range in the stabilization of these non-equilibrium phases of matter that break the discrete time-translational symmetry of a periodic drive.
The relaxation of uniform quantum systems with finite-range interactions after a quench is generically driven by the ballistic propagation of long-lived quasi-particle excitations triggered by a sufficiently small quench. Here we investigate the case of long-range ($1/r^α$) interactions for $d$-dimensional lattice spin models with uniaxial symmetry, and show that, in the regime $d < α< d+2$, the entanglement and correlation buildup is radically altered by the existence of a non-linear dispersion relation of quasi-particles, $ω\sim k^{z<1}$, at small wave vectors, leading to a divergence of the…
Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as useful experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as $1/r^α$ with $α> d/2$. We show that the disordered averaged energy …
The conventional framework for defining and understanding phases of matter requires thermodynamic equilibrium. Extensions to non-equilibrium systems have led to surprising insights into the nature of many-body thermalization and the discovery of novel phases of matter, often catalyzed by driving the system periodically. The inherent heating from such Floquet drives can be tempered by including strong disorder in the system, but this can also mask the generality of non-equilibrium phases. In this work, we utilize a trapped-ion quantum simulator to observe signatures of a non-equilibrium driven …
As realized by Kapitza long ago, a rigid pendulum can be stabilized upside down by periodically driving its suspension point with tuned amplitude and frequency. While this dynamical stabilization is feasible in a variety of instances in systems with few degrees of freedom, it is natural to search for generalizations to multi-particle systems. In particular, a fundamental question is whether, by periodically driving a single parameter in a many-body system, one can stabilize an otherwise unstable phase of matter against all possible fluctuations of its microscopic degrees of freedom. In this wo…
Emergent Self-Similar Quantum Revivals in Spiral Drives
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Princeton University（普林斯顿大学）；Peking University（北京大学）；École Normale Supérieure (ENS), Université PSL（巴黎高等师范学院，PSL大学）
Large-scale simulations on three-dimensional (3D) frustrated anisotropic XY model have been performed to study the nonequilibrium phase transitions of vortex matter in weak random pinning potential in layered superconductors. The first-order phase transition from the moving Bragg glass to the moving smectic is clarified, based on thermodynamic quantities. A washboard noise is observed in the moving Bragg glass in 3D simulations for the first time. It is found that the activation of the vortex loops play the dominant role in the dynamical melting at high drive.
The glass transition, extensively studied in dense fluids, polymers, or colloids, corresponds to a dramatic evolution of equilibrium transport coefficients upon a modest change of control parameter, like temperature or pressure. A similar phenomenology is found in many systems evolving far from equilibrium, such as driven granular media, active and living matter. While many theories compete to describe the glass transition at thermal equilibrium, very little is understood far from equilibrium. Here, we solve the dynamics of a specific, yet representative, class of glass models in the presence …
Matter agglomeration mesoscopic phenomena of irreversible type are well described by nonequilibrium thermodynamics formalism. The description assumes that the thermodynamic (internal) state variables are in local equilibrium, and uses the well known flux-force relations, with the Onsager coefficients involved, ending eventually up at a local conservation law of Fokker-Planck type. One of central problems arising when applying it to the matter agglomeration phenomena, quite generally termed nucleation-and-growth process, appears to be some physically accepted identification of entropic barriers…
Laser technology has developed and accelerated photo-induced nonequilibrium physics from both scientific and engineering viewpoints. The Floquet engineering, i.e., controlling material properties and functionalities by time-periodic drives, is a forefront of quantum physics of light-matter interaction, but limited to ideal dissipationless systems. For the Floquet engineering extended to a variety of materials, it is vital to understand the quantum states emerging in a balance of the periodic drive and energy dissipation. Here we derive the general description for nonequilibrium steady states (…
A defining feature of living matter is the ability to harness energy to self-organize multiscale structures whose functions are facilitated by irreversible nonequilibrium dynamics. While progress has been made in elucidating the underlying principles, what remains unclear is the role that thermodynamics plays in shaping these structures and their ensuing functions. Here, we unravel how a fundamental thermodynamic connection between the physical energy dissipation sustaining a nonequilibrium system and a measure of statistical irreversibility (arrow of time), can provide quantitative insight in…
Depinning and nonequilibrium transitions within sliding states in systems driven over quenched disorder arise across a wide spectrum of size scales ranging from atomic friction at the nanoscale, flux motion in type-II superconductors at the mesoscale, colloidal motion in disordered media at the microscale, and plate tectonics at geological length scales. Here we show that active matter or self-propelled particles interacting with quenched disorder under an external drive represents a new class of system that can also exhibit pinning-depinning phenomena, plastic flow phases, and nonequilibrium …
Active matter, comprising many active agents interacting and moving in fluids or more complex environments, is a commonly occurring state of matter in biological and physical systems. By its very nature active matter systems exist in nonequilibrium states. In this paper the active agents are small Janus colloidal particles that use chemical energy provided by chemical reactions occurring on their surfaces for propulsion through a diffusiophoretic mechanism. As a result of interactions among these colloids, either directly or through fluid velocity and concentration fields, they may act collect…
We show that "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- belong to a new universality class in spatial dimensions $d>2$. We calculate the universal exponents and scaling laws of this new universality class to $O(ε)$ in a $d=4-ε$ expansion, and find these are different from the "canonical" exponents previously conjectured to hold for "immortal" flocks (i.e., those without birth and death) and shown to hold for incompressible flocks with spatial dimensions in the range o…
We present the results of a detailed study of energy correlations at steady state for a 1-D model of coupled energy and matter transport. Our aim is to discover -- via theoretical arguments, conjectures, and numerical simulations -- how spatial covariances scale with system size, their relations to local thermodynamic quantities, and the randomizing effects of heat baths. Among our findings are that short-range covariances respond quadratically to local temperature gradients, and long-range covariances decay linearly with macroscopic distance. These findings are consistent with exact results f…
We present a general, model-independent, quantum statistical treatment of the connection between the quantum and hydrodynamical pictures of reservoir driven macroscopic systems. This treatment is centred on the large scale properties of locally conserved hydrodynamical observables and is designed to form a bridge between quantum microdynamics and classical macroscopic continuum mechanics, rather than a derivation of the latter from the former. The key assumptions on which the treatment is based are hypotheses of chaoticity and local equilibrium for the hydrodynamical fluctuations around nonequ…
The local equilibrium approach previously developed by the Authors [J. Mabillard and P. Gaspard, J. Stat. Mech. (2020) 103203] for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and their local thermodynamic and transport properties are deduced from the microscopic Hamiltonian dynamics. In particular, the Green-Kubo formulas are obtained for all the transport coefficients. The eight hydrodynamic modes and their dispersion relation are studied for general and cubic crystals. In the same twenty crystallographic classes as those compatibl…
Abstract: Models for studying systems in stationary states but out of equilibrium have often empirical nature and very often break the fundamental time reversal symmetry. Here a formal interpretation will be discussed of the widespread idea that, in any event, the particular friction model choice should not matter physically. The proposal is, quite generally, that for the same physical system a time reversible model should be possible. Examples about the Navier-Stokes equations are given.
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also rapidly sample uncorrelated configurations. Here, we introduce a new class of moves based on nonequilibrium dynamics: candidate configurations are generated through a finite-time process in which a system is actively driven out of equilibrium, and accepted with criteria that preserve the equilibrium distribution. The acceptance rule is similar to the Metropoli…
In active $φ^4$ field theories the nonequilibrium terms play an important role in describing active phase separation; however, they are irrelevant, in the renormalization group sense, at the critical point. Their irrelevance makes the critical exponents the same as those of the Ising universality class. Despite their irrelevance, they contribute to a nontrivial scaling of the entropy production rate at criticality. We consider the nonequilibrium dynamics of a nonconserved scalar field $φ$ (Model A) driven out-of-equilibrium by a persistent noise that is correlated on a finite timescale $τ$, as…
First-order nonequilibrium phase transitions observed in active matter, fluid dynamics, biology, climate science, and other systems with irreversible dynamics are challenging to analyze because they cannot be inferred from a simple free energy minimization principle. Rather the mechanism of these transitions depends crucially on the system's dynamics, which requires us to analyze them in trajectory space rather than in phase space. Here we consider situations where the path of these transitions can be characterized as the minimizer of an action, whose minimum value can be used in a nonequilibr…
