The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation

Abstract

The Středa formula establishes a fundamental connection between the topological invariants characterizing the bulk of topological matter and the presence of gapless edge modes. In this work, we extend the Středa formula to periodically driven systems, providing a rigorous framework to elucidate the unconventional bulk-boundary correspondence of Floquet systems, while offering a link between Floquet winding numbers and tractable response functions. Using the Sambe representation of periodically driven systems, we analyze the response of the unbounded Floquet density of states to a magnetic perturbation. This Floquet-Středa response is regularized through Cesàro summation, yielding a well-defined, quantized result within spectral gaps. The response features two physically distinct contributions: a quantized charge flow between edge and bulk, and an anomalous energy flow between the system and the drive, offering new insight into the nature of anomalous edge states. This result rigorously connects Floquet winding numbers to the orbital magnetization density of Floquet states and holds broadly, from clean to disordered and inhomogeneous systems. This is further supported by providing a real-space formulation of the Floquet-Středa response, which introduces a local topological marker suited for periodically driven settings. In translationally-invariant systems, the framework yields a remarkably simple expression for Floquet winding numbers involving geometric properties of Floquet-Bloch bands. A concrete experimental protocol is proposed to extract the Floquet-Středa response via particle-density measurements in systems coupled to engineered baths. Finally, by expressing the topological invariants through the magnetic response of the Floquet density of states, this approach opens a promising route toward the topological characterization of interacting driven phases.

34 pages, 16 figures

References in corpus (149)

• Topological Insulators
• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Topological Photonics
• Photonic Floquet Topological Insulators
• Experimental realisation of the topological Haldane model
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Topological Materials: Weyl Semimetals
• Topological quantum chemistry
• Topological superconductors: a review
• Photovoltaic Hall effect in graphene
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Observation of Floquet-Bloch states on the surface of a topological insulator
• Topological characterization of periodically-driven quantum systems
• Atomic quantum gases in periodically driven optical lattices
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Floquet Engineering of Quantum Materials
• Topological Bands for Ultracold Atoms
• On the phase structure of driven quantum systems
• Light-induced anomalous Hall effect in graphene
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Nonequilibrium dynamical mean-field theory and its applications
• Signatures of Fractional Quantum Anomalous Hall States in Twisted MoTe2 Bilayer
• High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
• Quantum simulation of frustrated magnetism in triangular optical lattices
• Dynamical control of matter-wave tunneling in periodic potentials
• Floquet Topological Insulators for Sound
• Observation of topologically protected bound states in a one dimensional photonic system
• Berry phase correction to electron density of states in solids
• Fractional Chern insulators in magic-angle twisted bilayer graphene
• Equilibrium states of generic quantum systems subject to periodic driving
• Observation of photonic anomalous Floquet Topological Insulators
• Long-time behavior of periodically driven isolated interacting lattice systems
• Chiral groundstate currents of interacting photons in a synthetic magnetic field
• Fractional quantum Hall states of atoms in optical Lattices
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Topologically protected acoustic helical edge states and interface states in strongly coupled metamaterial ring lattices
• Orbital magnetization in periodic insulators
• Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
• Selective scattering between Floquet-Bloch and Volkov states in a topological insulator
• Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon
• Irradiated graphene as a tunable Floquet topological insulator
• Periodic Table for Floquet Topological Insulators
• Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
• Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals
• Realization of an anomalous Floquet topological system with ultracold atoms
• Floquet chiral edge states in graphene
• Topological singularities and the general classification of Floquet-Bloch systems
• Mapping topological order in coordinate space
• Quantum Theory of Orbital Magnetization and its Generalization to Interacting Systems
• Microscopy of the interacting Harper-Hofstadter model in the few-body limit
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Equilibration and Order in Quantum Floquet Matter
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Effective Hamiltonians for periodically driven systems
• Bulk--Boundary Correspondence for Chiral Symmetric Quantum Walks
• Multiterminal Conductance of a Floquet Topological Insulator
• The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
• Out of equilibrium electrons and the Hall conductance of a Floquet topological insulator
• Classification of Interacting Topological Floquet Phases in One Dimension
• Classification of topological phases in periodically driven interacting systems
• Topology and Broken Symmetry in Floquet Systems
• Pseudospin-selective Floquet band engineering in black phosphorus
• Transport signatures of Floquet Majorana fermions in driven topological superconductors
• Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
• Symmetries, Topological Phases and Bound States in the One-Dimensional Quantum Walk
• Measuring topology by dynamics: Chern number from linking number
• Correlated electron systems periodically driven out of equilibrium: Floquet + DMFT formalism
• Tailoring quantum gases by Floquet engineering
• Controlled Population of Floquet-Bloch States via Coupling to Bose and Fermi Baths
• Observation of anomalous π modes in photonic Floquet engineering
• Measuring quantized circular dichroism in ultracold topological matter
• Optical response of graphene under intense terahertz fields
• Index theory of one dimensional quantum walks and cellular automata
• Realization of a fractional quantum Hall state with ultracold atoms
• Chiral Floquet Phases of Many-body Localized Bosons
• Hierarchy of Floquet gaps and edge states for driven honeycomb lattices
• Electromagnetic coupling in tight-binding models for strongly correlated light and matter
• Measurement of a topological edge invariant in a microwave network
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Abelian Floquet symmetry-protected topological phases in one dimension
• Occupation of topological Floquet bands in open systems
• Cavity Quantum-Electrodynamical Chern Insulator: Route Towards Light-Induced Quantized Anomalous Hall Effect in Graphene
• Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator
• Floquet Topological Order in Interacting Systems of Bosons and Fermions
• Anomalous Floquet Insulators
• Topological Floquet-Thouless energy pump
• Steady Floquet-Andreev States Probed by Tunnelling Spectroscopy
• Unpaired Floquet Majorana fermions without magnetic fields
• Interacting invariants for Floquet phases of fermions in two dimensions
• Observation of Floquet states in graphene
• Topological classification of quasi-periodically driven quantum systems
• Topological Marker Currents in Chern Insulators
• Steady states and edge state transport in topological Floquet-Bloch systems
• Quantized magnetization density in periodically driven systems
• Quantum to classical crossover of Floquet engineering in correlated quantum systems
• Engineering and probing non-Abelian chiral spin liquids using periodically driven ultracold atoms
• Observation of pi/2 modes in an acoustic Floquet system
• Non-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator
• Tuning anomalous Floquet topological bands with ultracold atoms
• Mott insulators with boundary zeros
• Photon Inhibited Topological Transport in Quantum Well Heterostructures
• Edge State Transport in Floquet Topological Insulators
• Direct observation of Floquet-Bloch states in monolayer graphene
• Wannier representation of Floquet topological states
• Quantum Floquet engineering with an exactly solvable tight-binding chain in a cavity
• Theory of Non-Equilibirum States Driven by Constant Electromagnetic Fields: Non-Commutative Quantum Mechanics in the Keldysh Formalism
• Unified Formalism for calculating Polarization, Magnetization, and more in a Periodic Insulator
• Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
• Topological interpretation of Luttinger theorem
• Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect
• How to Directly Measure Floquet Topological Invariants in Optical Lattices
• Cavity Light-Matter Entanglement through Quantum Fluctuations
• Real-space detection and manipulation of topological edge modes with ultracold atoms
• Classification of Matrix-Product Unitaries with Symmetries
• Quantized topological energy pumping and Weyl points in Floquet synthetic dimensions with a driven-dissipative photonic molecule
• Kibble-Zurek behavior in disordered Chern insulators
• Positivity of the spectral densities of retarded Floquet Green functions
• Quantized large-bias current in the anomalous Floquet-Anderson insulator
• Connecting the Many-Body Chern Number to Luttinger's Theorem through Středa's Formula
• Quantum annealing and non-equilibrium dynamics of Floquet Chern insulators
• Topological properties of Floquet winding bands in a photonic lattice
• Floquet engineering topological Dirac bands
• The Fermi-Dirac staircase occupation of Floquet bands and current rectification inside the optical gap of metals: a rigorous perspective
• Electron-photon Chern number in cavity-embedded 2D moiré materials
• Berry Phase and Topology in Ultrastrongly Coupled Quantum Light-Matter Systems
• Loading Ultracold Gases in Topological Floquet Bands: Current and Center-of-Mass Responses
• Counter-propagating edge states in Floquet topological insulating phases
• Cavity Induced Topology in Graphene
• Spectral flow and global topology of the Hofstadter butterfly
• Hierarchy of many-body invariants and quantized magnetization in anomalous Floquet insulators
• Time-resolved Hall conductivity of pulse-driven topological quantum systems
• Effective response theory for Floquet topological systems
• The Floquet Fermi Liquid
• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Dynamical Detection of Topological Spectral Density
• Josephson-Current Signatures of Unpaired Floquet Majorana Bound States
• Theory of Interacting Bloch Electrons in a Magnetic Field
• Semiclassical dynamics of electrons in space-time crystal: Magnetization, polarization, and current response
• Floquet-heating-induced Bose condensation in a scar-like mode of an open driven optical-lattice system
• Periodically driven interacting electrons in 1D: a many-body Floquet approach
• Anomalous Floquet Phases. A resonance phenomena
• Edge-dependent anomalous topology in synthetic photonic lattices subject to discrete step walks
• Quantum state preparation of topological chiral spin liquids via Floquet engineering
• Light-matter correlations in Quantum Floquet engineering of cavity quantum materials
• Dissipative preparation of a Floquet topological insulator in an optical lattice via bath engineering
• Floquet dynamical chiral spin liquid at finite frequency
• Quantized valley Hall response from local bulk density variations

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• Average density of Bloch electrons in a homogeneous magnetic field: A second-order response
• Quantized Chern-Simons Axion Coupling in Anomalous Floquet Systems