Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs

Abstract

Recent work suggests that a sharp definition of `phase of matter' can be given for some quantum systems out of equilibrium---first for many-body localized systems with time independent Hamiltonians and more recently for periodically driven or Floquet localized systems. In this work we propose a classification of the finite abelian symmetry protected phases of interacting Floquet localized systems in one dimension. We find that the different Floquet phases correspond to elements of $\text{Cl}\times {\mathcal{A}}_G$, where $\text{Cl}$ is the undriven interacting classification, and ${\mathcal{A}}_G$ is a set of (twisted) 1d representations of $G$. We will address symmetry broken phases in a subsequent paper.

21 pages. Explained connection to the classification schemes in other recent work. Close to published version

References in corpus (13)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological characterization of periodically-driven quantum systems
• Phenomenology of fully many-body-localized systems
• Equilibrium states of generic quantum systems subject to periodic driving
• Many-body localization in periodically driven systems
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Disorder-induced Floquet Topological Insulators
• Classification of topological phases in periodically driven interacting systems
• 1D Many-body localized Floquet systems II: Symmetry-Broken phases
• Topological index for periodically driven time-reversal invariant 2D systems
• Quantum criticality of hot random spin chains
• Protection of topological order by symmetry and many-body localization
• Effects of Disorder on a 1-D Floquet Symmetry Protected Topological Phase

Cited by in corpus (179)

• Many-body localization, thermalization, and entanglement
• Topological phases of non-Hermitian systems
• Observation of a Discrete Time Crystal
• Floquet Time Crystals
• Time crystals: a review
• Periodic Table for Floquet Topological Insulators
• Discrete Time Crystals
• Periodically Driving a Many-Body Localized Quantum System
• Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
• Pre-thermal phases of matter protected by time-translation symmetry
• Equilibration and Order in Quantum Floquet Matter
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• Classification of Interacting Topological Floquet Phases in One Dimension
• Topology and Broken Symmetry in Floquet Systems
• Tenfold Way for Quadratic Lindbladians
• 1D Many-body localized Floquet systems II: Symmetry-Broken phases
• Colloquium: Quantum and Classical Discrete Time Crystals
• Gauging spatial symmetries and the classification of topological crystalline phases
• Confined Quasiparticle Dynamics in Long-Range Interacting Quantum Spin Chains
• Topological frequency conversion in strongly driven quantum 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
• Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
• Observation of a symmetry-protected topological time crystal with superconducting qubits
• Abelian Floquet symmetry-protected topological phases in one dimension
• Symmetry constraints on many-body localization
• A Floquet Model for the Many-Body Localization Transition
• Floquet topological phases protected by time glide symmetry
• Long-range entanglement from measuring symmetry-protected topological phases
• Floquet topological phases with symmetry in all dimensions
• Floquet Topological Order in Interacting Systems of Bosons and Fermions
• Long-Range Prethermal Phases of Nonequilibrium Matter
• Radical chiral Floquet phases in a periodically driven Kitaev model and beyond
• Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems
• Logarithmically Slow Relaxation in Quasi-Periodically Driven Random Spin Chains
• Realizing a dynamical topological phase in a trapped-ion quantum simulator
• Topology of one dimensional quantum systems out of equilibrium
• ${}^{31}$P NMR study of discrete time-crystalline signatures in an ordered crystal of ammonium dihydrogen phosphate
• Many-body localization, symmetry, and topology
• Anomalous Floquet Insulators
• Topological Floquet-Thouless energy pump
• Critical Phenomena and Kibble-Zurek Scaling in the Long-Range Quantum Ising Chain
• Many-body localization beyond eigenstates in all dimensions
• Interacting invariants for Floquet phases of fermions in two dimensions
• Space-time crystal and space-time group
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories: Part I
• Driving induced many-body localization
• Steady states and edge state transport in topological Floquet-Bloch systems
• Dynamically enriched topological orders in driven two-dimensional systems
• Quantized magnetization density in periodically driven systems
• Integrable many-body quantum Floquet-Thouless pumps
• Classification of topological insulators and superconductors out of equilibrium
• Time crystal behavior of excited eigenstates
• Mixed-state long-range order and criticality from measurement and feedback
• Topologically protected braiding in a single wire using Floquet Majorana modes
• Floquet Quantum Criticality
• Learning phase transitions from dynamics
• Floquet Phases of Matter via Classical Prethermalization
• Emergent Spatial Structure and Entanglement Localization in Floquet Conformal Field Theory
• Prethermal time crystals in a one-dimensional periodically driven Floquet system
• Topological Time Crystals
• Floquet conformal field theories with generally deformed Hamiltonians
• Minimalist approach to the classification of symmetry protected topological phases
• Probing quantum thermalization of a disordered dipolar spin ensemble with discrete time-crystalline order
• Floquet Dynamics of Boundary-Driven Systems at Criticality
• Absence of Thermalization in Finite Isolated Interacting Floquet Systems
• Universal chiral quasi-steady states in periodically driven many-body systems
• Localization and symmetry breaking in the quantum quasiperiodic Ising glass
• Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains
• Emergent hydrodynamics in non-equilibrium quantum systems
• Parafermion chain with $2\pi /k$ Floquet edge modes
• Matrix Product Representation of Locality Preserving Unitaries
• Almost strong 0, π edge modes in clean, interacting 1D Floquet systems
• Floquet Hopf Insulators
• Half-integer quantized topological response in quasiperiodically driven quantum systems
• Steady state of interacting Floquet insulators
• Topological Frequency Conversion in a Driven Dissipative Quantum Cavity
• Classification of $S{L}_2$ deformed Floquet Conformal Field Theories
• Quantum time crystals with programmable disorder in higher dimensions
• Geometric aspects of nonlinear and nonequilibrium phenomena
• Spin and topological order in a periodically driven spin chain
• Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system
• Absolutely Stable Spatiotemporal Order in Noisy Quantum Systems
• Quasiperiodic Floquet-Thouless energy pump
• Disorder induced transitions in resonantly driven Floquet Topological Insulators
• Classification of Matrix-Product Unitaries with Symmetries
• Stark time crystals: Symmetry breaking in space and time
• Quantized large-bias current in the anomalous Floquet-Anderson insulator
• Statistical Mechanics of Floquet Quantum Matter: Exact and Emergent Conservation Laws
• Periodically, Quasi-periodically, and Randomly Driven Conformal Field Theories (II): Furstenberg's Theorem and Exceptions to Heating Phases
• Signatures and conditions for phase band crossings in periodically driven integrable systems
• The Fermi-Dirac staircase occupation of Floquet bands and current rectification inside the optical gap of metals: a rigorous perspective
• The Floquet Engineer's Handbook
• Topological edge modes without symmetry in quasiperiodically driven spin chains
• Topology and localization of a periodically driven Kitaev model
• Classification of interacting Floquet phases with $U(1)$ symmetry in two dimensions
• Fermionic quantum cellular automata and generalized matrix product unitaries
• Disordered Chern insulator with a two step Floquet drive
• Observing Floquet topological order by symmetry resolution
• On adiabatic cycles of quantum spin systems
• Eigenstate phases with finite on-site non-Abelian symmetry
• Entanglement properties of the time periodic Kitaev Chain
• Stability of Periodically Driven Topological Phases against Disorder
• Universal presence of time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators
• Interacting Symmetry-Protected Topological Phases Out of Equilibrium
• Floquet Prethermal Phase Protected by U(1) Symmetry on a Superconducting Quantum Processor
• A UV perspective on mixed anomalies at critical points between bosonic symmetry-protected phases
• Hierarchy of many-body invariants and quantized magnetization in anomalous Floquet insulators
• String order parameters for 1d Floquet Symmetry Protected Topological Phases
• Many-body dynamics and gap opening in interacting periodically driven systems
• The Real-Time Correlation Function of Floquet Conformal Fields
• Strong-Disorder Renormalization Group for Periodically Driven Systems
• Tracking the quantized information transfer at the edge of a chiral Floquet phase
• Fractionalized Prethermalization in a Driven Quantum Spin Liquid
• Effective response theory for Floquet topological systems
• Chiral Flow in One-dimensional Floquet Topological Insulators
• Critical properties of the Floquet time crystal within the Gaussian approximation
• Prethermalization and entanglement dynamics in interacting topological pumps
• Strong zero modes in integrable quantum circuits
• Time-crystalline Topological Superconductors
• Stability of Floquet Majorana box qubits
• An infinite family of 3d Floquet topological paramagnets
• Anomalous topological edge modes in a periodically-driven trimer lattice
• Quantized Floquet topology with temporal noise
• Dynamical enhancement of symmetries in many-body systems
• Topological Defects in Floquet Circuits
• Floquet Supersymmetry
• Density-Matrix Renormalization Group study of Many-Body Localization in Floquet Eigenstates
• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
• Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena
• Interacting Floquet topological phases in three dimensions
• Unitary Subharmonic Response and Floquet Majorana Modes
• Electronic Floquet Liquid Crystals
• Non-adiabatic bulk-surface oscillations in driven topological insulators
• Gauging anomalous unitary operators
• Generalized Thouless Pumps in 1+1-dimensional Interacting Fermionic Systems
• Statistically induced topological phase transitions in a one-dimensional superlattice anyon-Hubbard model
• Dynamical Fragile Topology in Floquet Crystals
• Long-lived coherence in driven spin systems: from two to infinite spatial dimensions
• The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation
• Exponentially long lifetime of universal quasi-steady states in topological Floquet pumps
• Robust spectral $\pi$ pairing in the random-field Floquet quantum Ising model
• Response of a quantum disordered spin system to a local periodic drive
• Topologically protected boundary discrete time crystal for a solvable model
• Gappability Index for Quantum Many-Body Systems
• Electron Interaction Effects in Periodically Driven Kitaev Model: Topology Breaking and Enhancement of Quantum Chaos
• Localisation Transition in the Driven Aubry-André Model
• Floquet chiral hinge modes and their interplay with Weyl physics in a three-dimensional lattice
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
• Topologically ordered time crystals
• Dynamical potentials for non-equilibrium quantum many-body phases
• Topological excitations at time vortices in periodically driven systems
• Quantum quench in a driven Ising chain
• Topological phases of unitary dynamics: Classification in Clifford category
• Holographic Dynamics from Multiscale Entanglement Renormalization Ansatz
• Relation between scattering matrix topological invariants and conductance in Floquet Majorana systems
• Phase Transitions and Conductivties of Floquet Fluids
• Floquet Product Mode
• Moment method and continued fraction expansion in Floquet Operator Krylov Space
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• Properties of dissipative Floquet Majorana modes using a quantum dot
• The Symmetry Principle in Condensed Matter Physics (I)
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Scaling of Loschmidt echo in boundary driven critical Z-3 Potts model
• $2+1$ dimensional Floquet systems and lattice fermions: Exact bulk spectral equivalence
• Strong and almost strong modes of Floquet spin chains in Krylov subspaces
• Discrete time crystals detected by time-translation twist
• Adiabatic modulation of driving protocols in periodically driven quantum systems
• Anderson Localisation for periodically driven systems
• SPT extension of $Z_2$ quantum Ising model's ferromagnetic phase
• Floquet operator dynamics and orthogonal polynomials on the unit circle
• Dynamical Symmetry Indicators for Floquet Crystals
• Orbital magnetization of Floquet topological systems
• Floquet topological systems with flat bands: Edge modes, Berry curvature, and Orbital magnetization
• Engineering micromotion in Floquet prethermalization via space-time symmetries
• Noise resilience of two-dimensional Floquet topological phases
• Noninvertible Kramers-Wannier duality symmetries for the discrete-time quantum Ising chain