Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems

Abstract

We show how a large family of interacting nonequilibrium phases of matter can arise from the presence of multiple time-translation symmetries, which occur by quasiperiodically driving an isolated quantum many-body system with two or more incommensurate frequencies. These phases are fundamentally different from those realizable in time-independent or periodically-driven (Floquet) settings. Focusing on high-frequency drives with smooth time-dependence, we rigorously establish general conditions for which these phases are stable in a parametrically long-lived `preheating' regime. We develop a formalism to analyze the effect of the multiple time-translation symmetries on the dynamics of the system, which we use to classify and construct explicit examples of the emergent phases. In particular, we discuss time quasi-crystals which spontaneously break the time-translation symmetries, as well as time-translation symmetry protected topological phases.

arXiv comment27 pages + 11 pages appendices. v3 Published version, with expanded discussion on a few points

References in corpus (111)

• Topological Insulators
• Topological insulators and superconductors
• Many-Body Physics with Ultracold Gases
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Anyons in an exactly solved model and beyond
• Chaos and Quantum Thermalization
• The nitrogen-vacancy colour centre in diamond
• Many body localization and thermalization in quantum statistical mechanics
• Many-body localization, thermalization, and entanglement
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Atomic quantum gases in periodically driven optical lattices
• Observation of a Discrete Time Crystal
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Exploring the many-body localization transition in two dimensions
• Floquet Time Crystals
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Topological Bands for Ultracold Atoms
• State preservation by repetitive error detection in a superconducting quantum circuit
• On the phase structure of driven quantum systems
• Zoo of quantum-topological phases of matter
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Classifying quantum phases using Matrix Product States and PEPS
• Many-body localization: an introduction and selected topics
• Many-body localization in a disordered quantum Ising chain
• Discrete time crystals: rigidity, criticality, and realizations
• Symmetry Protected Topological phases of Quantum Matter
• Braiding statistics approach to symmetry-protected topological phases
• Equilibrium states of generic quantum systems subject to periodic driving
• Long-time behavior of periodically driven isolated interacting lattice systems
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Area laws in a many-body localized state and its implications for topological order
• Spectral signatures of many-body localization with interacting photons
• Experimental observation of the Anderson transition with atomic matter waves
• Localization protected quantum order
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• Exponentially slow heating in periodically driven many-body systems
• Fate of many-body localization under periodic driving
• Stability and instability towards delocalization in MBL systems
• Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems
• Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Periodically driven ergodic and many-body localized quantum systems
• Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
• A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
• Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
• Pre-thermal phases of matter protected by time-translation symmetry
• Equilibration and Order in Quantum Floquet Matter
• Floquet Fractional Chern Insulator in Doped Graphene
• Stark many-body localization
• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
• Classification of Interacting Topological Floquet Phases in One Dimension
• Classification of topological phases in periodically driven interacting systems
• Symmetry protected topological phases from decorated domain walls
• From Bloch Oscillations to Many Body Localization in Clean Interacting Systems
• Many-body Localization and Symmetry Protected Topological Order
• The Hilbert-glass transition: new universality of temperature-tuned many-body dynamical quantum criticality
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Observation of time quasicrystal and its transition to superfluid time crystal
• Dynamical quantum phase transitions in random spin chains
• A theory of many-body localization in periodically driven systems
• 1D Many-body localized Floquet systems II: Symmetry-Broken phases
• How a small quantum bath can thermalize long localized chains
• Quantum quenches in the many-body localized phase
• Floquet engineering of correlated tunneling in the Bose-Hubbard model with ultracold atoms
• Statistical localization: from strong fragmentation to strong edge modes
• Critical thermalization of a disordered dipolar spin system in diamond
• Gauging spatial symmetries and the classification of topological crystalline phases
• Topological frequency conversion in strongly driven quantum systems
• Critical Time Crystals in Dipolar Systems
• Chiral Floquet Phases of Many-body Localized Bosons
• Floquet prethermalization and regimes of heating in a periodically driven, interacting quantum system
• Floquet symmetry-protected topological phases in cold atomic systems
• Between a metal and an insulator: the critical state of the Anderson transition
• Quasiperiodically driven ratchets for cold atoms
• Time Quasi-periodic unbounded perturbations of Schrödinger operators and KAM methods
• Abelian Floquet symmetry-protected topological phases in one dimension
• Floquet topological phases with symmetry in all dimensions
• Floquet Topological Order in Interacting Systems of Bosons and Fermions
• Onset of Floquet Thermalisation
• Long-Range Prethermal Phases of Nonequilibrium Matter
• Period-$n$ discrete time crystals and quasicrystals with ultracold bosons
• Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin Chains
• Radical chiral Floquet phases in a periodically driven Kitaev model and beyond
• Many-body localization, symmetry, and topology
• Symmetry-protected topological invariants of symmetry-protected topological phases of interacting bosons and fermions
• Crystalline topological phases as defect networks
• Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
• Prethermal Strong Zero Modes and Topological Qubits
• Many-Body Localization: Stability and Instability
• Discrete Time Quasi-Crystals
• Interacting invariants for Floquet phases of fermions in two dimensions
• Topological classification of quasi-periodically driven quantum systems
• Dynamically enriched topological orders in driven two-dimensional systems
• Aperiodically driven integrable systems and their emergent steady states
• Quasi-periodically driven quantum systems
• Floquet Mechanism for Non-Abelian Fractional Quantum Hall States
• Minimalist approach to the classification of symmetry protected topological phases
• Probing quantum thermalization of a disordered dipolar spin ensemble with discrete time-crystalline order
• Time-quasiperiodic topological superconductors with Majorana Multiplexing
• Floquet Time Spirals and Stable Discrete Time Quasi-Crystals in Quasi-Periodically Driven Quantum Many-Body Systems
• Universal chiral quasi-steady states in periodically driven many-body systems
• Topological Frequency Conversion in a Driven Dissipative Quantum Cavity
• Bounds on Energy Absorption and Prethermalization in Quantum Systems with Long-Range Interactions
• Steady states of a quasiperiodically driven integrable system
• Dynamics of quasiperiodically driven spin systems
• Locality and Heating in Periodically Driven, Power-law Interacting Systems
• Control of transport in higher dimensional systems via dynamical decoupling of degrees of freedom with quasiperiodic driving fields
• Asymptotic theory of quasiperiodically driven quantum systems

Cited by in corpus (72)

• Localization from Hilbert space shattering: from theory to physical realizations
• Local constraints can globally shatter Hilbert space: a new route to quantum information protection
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
• Observation of a prethermal discrete time crystal
• Colloquium: Quantum and Classical Discrete Time Crystals
• Discrete time-crystalline order enabled by quantum many-body scars: entanglement steering via periodic driving
• Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals
• Transverse spin dynamics in the anisotropic Heisenberg model realized with ultracold atoms
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories: Part I
• Random multipolar driving: tunably slow heating through spectral engineering
• Speed limits and locality in many-body quantum dynamics
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Floquet Phases of Matter via Classical Prethermalization
• Nonadiabatic Topological Energy Pumps with Quasiperiodic Driving
• Scaling of temporal entanglement in proximity to integrability
• The fine structure of heating in a quasiperiodically driven critical quantum system
• Geometric aspects of nonlinear and nonequilibrium phenomena
• To heat or not to heat: time crystallinity and finite-size effects in clean Floquet systems
• Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems
• Quasiperiodic Floquet-Thouless energy pump
• Weak integrability breaking perturbations of integrable models
• Thermalization and Prethermalization in Periodically Kicked Quantum Spin Chains
• Quantum many-body topology of quasicrystals
• Quasi-Floquet prethermalization in a disordered dipolar spin ensemble in diamond
• Prethermalization and Thermalization in Periodically-Driven Many-Body Systems away from the High-Frequency Limit
• Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives
• Many-Body Localization with Quasiperiodic Driving
• Symmetry enhanced boundary qubits at infinite temperature
• Topological edge modes without symmetry in quasiperiodically driven spin chains
• A Floquet perturbation theory for periodically driven weakly-interacting fermions
• Dynamical relaxation of correlators in periodically driven integrable quantum systems
• Experimental Realization of Discrete Time Quasi-Crystals
• Non-Fermi liquids from kinetic constraints in tilted optical lattices
• Prethermalization and the local robustness of gapped systems
• Dynamical localization and slow dynamics in quasiperiodically-driven quantum systems
• Topological frequency conversion in Weyl semimetals
• Heating Rates under Fast Periodic Driving beyond Linear Response
• Dynamical localization and slow thermalization in a class of disorder-free periodically driven one-dimensional interacting systems
• Universal nonadiabatic energy pumping in a quasiperiodically driven extended system
• Localization persisting under aperiodic driving
• Exotic quantum liquids in Bose-Hubbard models with spatially-modulated symmetries
• Quantized Floquet topology with temporal noise
• Geometric Floquet theory
• Nonlocal discrete time crystals in periodically driven surface codes
• Hilbert-Space Ergodicity in Driven Quantum Systems: Obstructions and Designs
• Self-similar phase diagram of the Fibonacci-driven quantum Ising model
• Theory of metastable states in many-body quantum systems
• Anomalous Random Multipolar Driven Insulators
• Suppression of inter-band heating for random driving
• Absolutely stable time crystals at finite temperature
• Prethermalization in aperiodically driven classical spin systems
• Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics
• Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results
• A matrix product operator approach to non-equilibrium Floquet steady states
• Prethermalization in periodically-driven nonreciprocal many-body spin systems
• Prethermalization in the PXP Model under Continuous Quasiperiodic Driving
• Floquet-engineered Emergent Massive Nambu-Goldstone Modes
• Coupled Layer Construction for Synthetic Hall Effects in Driven Systems
• Topological frequency conversion in rhombohedral multilayer graphene
• Engineering Hierarchical Symmetries
• Energy cascade and Burgers turbulence in the Fermi-Pasta-Ulam-Tsingou chain
• Topological Phases of Many-Body Localized Systems: Beyond Eigenstate Order
• From time crystals to time quasicrystals: Exploring quasiperiodic phases in transverse field Ising chains
• Statistical prethermalization in randomly kicked many-body classical rotor system
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Stable time rondeau crystals in dissipative many-body systems
• Quantum Entanglement without nonlocal causation in (3,2)-dimensional spacetime
• Nonperturbative decay of bipartite discrete time crystals
• Quantized charge transport in disordered Floquet topological insulators in the absence of Anderson localization
• Engineering micromotion in Floquet prethermalization via space-time symmetries
• Fock space prethermalization and time-crystalline order on a quantum processor
• Emergence of prethermal time quasicrystalline order in a quasiperiodically driven non-interacting spin chain