Dynamic winding number for exploring band topology

Abstract

Topological invariants play a key role in the characterization of topological states. Due to the existence of exceptional points, it is a great challenge to detect topological invariants in non-Hermitian systems. We put forward a dynamic winding number, the winding of realistic observables in long-time average, for exploring band topology in both Hermitian and non-Hermitian two-band models via a unified approach. We build a concrete relation between dynamic winding numbers and conventional topological invariants. In one-dimension, the dynamical winding number directly gives the conventional winding number. In two-dimension, the Chern number relates to the weighted sum of dynamic winding numbers of all phase singularity points. This work opens a new avenue to measure topological invariants not requesting any prior knowledge of system topology via time-averaged spin textures.

arXiv comment6+7 pages, 3+4 figures

References in corpus (69)

• Topological insulators and superconductors
• Non-Abelian Anyons and Topological Quantum Computation
• Cavity Optomechanics
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Topological Photonics
• Classification of topological quantum matter with symmetries
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Experimental realisation of the topological Haldane model
• Edge states and topological invariants of non-Hermitian systems
• Topological Insulator Materials
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Symmetry and Topology in Non-Hermitian Physics
• Topological Band Theory for Non-Hermitian Hamiltonians
• Spintronics and Pseudospintronics in Graphene and Topological Insulators
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Topological energy transfer in an optomechanical system with exceptional points
• Non-Hermitian Chern bands
• Non-Hermitian Boundary Modes
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Biorthogonal Quantum Mechanics
• Edge states and topological phases in non-Hermitian systems
• Topological Transition in a Non-Hermitian Quantum Walk
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Experimental Observation of Three-Component 'New Fermions' in Topological Semimetal MoP
• New topological invariants in non-Hermitian systems
• Experimental realization of a Weyl exceptional ring
• Topological Quantum Computation Based on Chiral Majorana Fermions
• Dynamically encircling exceptional points: Exact evolution and polarization state conversion
• Observation of Zitterbewegung in a spin-orbit coupled Bose-Einstein condensate
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Topological invariance and global Berry phase in non-Hermitian systems
• Realization of 2D Spin-orbit Interaction and Exotic Topological Orders in Cold Atoms
• Measuring topology by dynamics: Chern number from linking number
• Dicke-type phase transition in a spin-orbit coupled Bose-Einstein condensate
• Uncover Topology by Quantum Quench Dynamics
• Measuring Topological Number of a Chern-Insulator from Quench Dynamics
• Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
• Dynamical classification of topological quantum phases
• Topological Phase Transitions and Thouless Pumping of Light in Photonic Waveguide Arrays
• Non-Hermitian Floquet topological phases with arbitrarily many real-quasienergy edge states
• Topological invariants and phase diagrams for one-dimensional two-band non-Hermitian systems without chiral symmetry
• Hall Conductance of a Non-Hermitian Chern Insulator
• High Controllable and Robust 2D Spin-Orbit Coupling for Quantum Gases
• Exceptional Points in a Non-Hermitian Topological Pump
• Non-Hermitian fractional quantum Hall states
• Band Topology, Orbital Phase Winding, and Selection Rules in Excitonic Physics in Two Dimensions
• Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator
• Dynamical detection of topological charges
• Detecting topological invariants in chiral symmetric insulators via losses
• Fixed points and emergent topological phenomena in a parity-time-symmetric quantum quench
• Dispersion Suppressed Topological Thouless Pumping
• Adiabatic Control of Atomic Dressed States for Transport and Sensing

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• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions
• Unified theory to characterize Floquet topological phases by quench dynamics
• Dual topological characterization of non-Hermitian Floquet phases
• Non-Hermitian Floquet Topological Matter -- A Review
• Dissipative Floquet Dynamical Quantum Phase Transition
• Non-Hermitian topological phases and dynamical quantum phase transitions: A generic connection
• Untying links through anti-parity-time-symmetric coupling
• Floquet engineering and simulating exceptional rings with a quantum spin system
• Observation of Floquet topological phases with large Chern numbers
• Double exceptional links in a three-dimensional dissipative cold atomic gas
• Universal topological quench dynamics: Altland-Zirnbauer tenfold classes
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
• Topological pumping assisted by Bloch oscillations
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Dynamically characterizing topological phases by high-order topological charges
• Topological edge states at Floquet quantum criticality
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Emergent topology and symmetry-breaking order in correlated quench dynamics
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Disorder-induced topology in quench dynamics
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Stability of dynamical topology against dynamical noise in quantum quenches
• Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• Generic theory of characterizing topological phases under quantum slow dynamics
• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Topological spin-orbit-coupled fermions beyond rotating wave approximation
• Entanglement phase transitions in non-Hermitian Kitaev chains
• Uncover band topology via quantized drift in two-dimensional Bloch oscillations
• Non-Hermitian dynamical topological winding in photonic mesh lattices
• Synthetic spin-orbit coupling for the multispin models in optical lattices
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Loop unitary and phase band topological invariant in generic multi-band Chern insulators
• $q$th-root non-Hermitian Floquet topological insulators
• Full investigation of nonadiabatic dynamical characterization in arbitrary quenching process