Topology and localization of a periodically driven Kitaev model
arXiv:1902.06995 · doi:10.1103/PhysRevB.99.235408
Abstract
Periodically driven quantum many-body systems support anomalous topological phases of matter, which cannot be realized by static systems. In many cases, these anomalous phases can be many-body localized, which implies that they are stable and do not heat up as a result of the driving. What types of anomalous topological phenomena can be stabilized in driven systems, and in particular, can an anomalous phase exhibiting non-Abelian anyons be stabilized? We address this question using an exactly solvable, stroboscopically driven 2D Kitaev spin model, in which anisotropic exchange couplings are boosted at consecutive time intervals. The model shows a rich phase diagram which contains anomalous topological phases. We characterize these phases using weak and strong scattering-matrix invariants defined for the fermionic degrees of freedom. Of particular importance is an anomalous phase whose zero flux sector exhibits fermionic bands with zero Chern numbers, while a vortex binds a pair of Majorana modes, which as we show support non-Abelian braiding statistics. We further show that upon adding disorder, the zero flux sector of the model becomes localized. However, the model does not remain localized for a finite density of vortices. Hybridization of Majorana modes bound to vortices form "vortex bands", which delocalize by either forming Chern bands or a thermal metal phase. We conclude that while the model cannot be many-body localized, it may still exhibit long thermalization times, owing to the necessity to create a finite density of vortices for delocalization to occur.
arXiv comment9 + 5 pages, 8 + 2 figures. This is the final, published version
References in corpus (78)
- Anyons in an exactly solved model and beyond
- Photonic Floquet Topological Insulators
- Experimental realisation of the topological Haldane model
- Anderson Transitions
- Floquet Topological Insulator in Semiconductor Quantum Wells
- Photovoltaic Hall effect in graphene
- Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
- Kwant: a software package for quantum transport
- Observation of Floquet-Bloch states on the surface of a topological insulator
- Topological characterization of periodically-driven quantum systems
- 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
- Floquet Time Crystals
- On the phase structure of driven quantum systems
- Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
- Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
- Observation of photonic anomalous Floquet Topological Insulators
- Long-time behavior of periodically driven isolated interacting lattice systems
- Topological Flat Band Models and Fractional Chern Insulators
- Floquet topological insulators
- Experimental observation of anomalous topological edge modes in a slowly-driven photonic lattice
- Exponentially slow heating in periodically driven many-body systems
- Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon
- Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
- Periodically driven ergodic and many-body localized quantum systems
- Topological singularities and the general classification of Floquet-Bloch systems
- Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
- Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
- Floquet Fractional Chern Insulator in Doped Graphene
- Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
- Disorder-induced Floquet Topological Insulators
- Floquet generation of Majorana end modes and topological invariants
- The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump
- Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
- Classification of Interacting Topological Floquet Phases in One Dimension
- Classification of topological phases in periodically driven interacting systems
- Transport signatures of Floquet Majorana fermions in driven topological superconductors
- Effective Theory of Floquet Topological Transitions
- Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
- Merging of Dirac points and Floquet topological transitions in AC driven graphene
- Scattering formula for the topological quantum number of a disordered multi-mode wire
- A theory of many-body localization in periodically driven systems
- Scattering theory of topological insulators and superconductors
- The insulator/Chern-insulator transition in the Haldane model
- Modulated Floquet Topological Insulators
- Topological index for periodically driven time-reversal invariant 2D systems
- Topological Floquet Spectrum in Three Dimensions via a Two-Photon Resonance
- Chiral Floquet Phases of Many-body Localized Bosons
- Adiabatic Perturbation Theory and Geometry of Periodically-Driven Systems
- Abelian Floquet symmetry-protected topological phases in one dimension
- Symmetry constraints on many-body localization
- Counter-propagating edge modes and topological phases of a kicked quantum Hall system
- Floquet Topological Order in Interacting Systems of Bosons and Fermions
- Radical chiral Floquet phases in a periodically driven Kitaev model and beyond
- Majorana edge modes in the Kitaev model
- Scattering matrix invariants of Floquet topological insulators
- Scattering theory of topological phases in discrete-time quantum walks
- Topological Superconducting Phases of Weakly Coupled Quantum Wires
- Topological indices, defects and Majorana fermion in chiral superconductors
- Materials design from non-equilibrium steady states: driven graphene as a tunable semiconductor with topological properties
- Quantized magnetization density in periodically driven systems
- Optical Control of Topological Quantum Transport in Semiconductors
- Electronic transport in an array of quasi-particles in the nu=5/2 non-abelian quantum Hall state
- Disorder-induced Majorana metal in interacting non-Abelian anyon systems
- Effective mass and tricritical point for lattice fermions localized by a random mass
- Perturbed vortex lattices and the stability of nucleated topological phases
- Band flatness optimization through complex analysis
- Majorana fermions on a disordered triangular lattice
- Equivalence of topological and scattering approaches to quantum pumping
- Extended topological group structure due to average reflection symmetry
- Thermal metal-insulator transition in a helical topological superconductor
- Braiding properties of Majorana Kramers Pairs
- Weak indices and dislocations in general topological band structures
- Dynamical manipulation of Dirac points in the Kitaev honeycomb model
- Transport in finite graphene samples
- Two-parameter scaling theory of transport near a spectral node
- Finite-size scaling in a 2D disordered electron gas with spectral nodes
- Floquet Majorana Edge Mode and Non-Abelian Anyons in a Driven Kitaev Model
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- Engineering and probing non-Abelian chiral spin liquids using periodically driven ultracold atoms
- Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
- Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium
- Probing non-equilibrium topological order on a quantum processor
- Cross-dimensional universality classes in static and periodically driven Kitaev models
- Fractionalized Prethermalization in a Driven Quantum Spin Liquid
- Counterdiabatic route for preparation of state with long-range topological order
- Anomalous levitation and annihilation in Floquet topological insulators
- Scalable quantum control and non-abelian anyon creation in the Kitaev honeycomb model
- Intermediate symmetric construction of transformation between anyon and Gentile statistics
- Quantum phase transitions and a disorder-based filter in a Floquet system
- Floquet engineering multi-channel Kondo physics
- Topological excitations at time vortices in periodically driven systems
- Topological reflection matrix
- Floquet dynamical chiral spin liquid at finite frequency
- Non-Linear Interference Challenging Topological Protection of Chiral Edge States
- Topological quantum phase transitions of anisotropic AFM Kitaev model driven by magnetic field
- Quantized charge transport in disordered Floquet topological insulators in the absence of Anderson localization
- A group method solving many-body systems in intermediate statistical representation
- Detuning the Floquet anomalous chiral spin liquid
- Fractionalized Prethermalization in the One-Dimensional Hubbard Model