Fixed points and emergent topological phenomena in a parity-time-symmetric quantum quench

Abstract

We identify emergent topological phenomena such as dynamic Chern numbers and dynamic quantum phase transitions in quantum quenches of the non-Hermitian Su-Schrieffer-Heeger Hamiltonian with parity-time ($\mathcal{P}\mathcal{T}$) symmetry. Their occurrence in the non-unitary dynamics are intimately connected with fixed points in the Brillouin zone, where the states do not evolve in time. We construct a theoretical formalism for characterizing topological properties in non-unitary dynamics within the framework of biorthogonal quantum mechanics, and prove the existence of fixed points for quenches between distinct static topological phases in the $\mathcal{P}\mathcal{T}$-symmetry-preserving regime. We then reveal the interesting relation between different dynamic topological phenomena through the momentum-time spin texture characterizing the dynamic process. For quenches involving Hamiltonians in the $\mathcal{P}\mathcal{T}$-symmetry-broken regime, these topological phenomena are not ensured.

arXiv comment6+5 pages; 4+3 figures; published in iScience

References in corpus (58)

• Topological Insulators
• Topological insulators and superconductors
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Experimental realisation of the topological Haldane model
• Edge states and topological invariants of non-Hermitian systems
• Complex Extension of Quantum Mechanics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological characterization of periodically-driven quantum systems
• Quantum many-body systems out of equilibrium
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Non-Hermitian Chern bands
• On the phase structure of driven quantum systems
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Dynamical quantum phase transitions: a review
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Topology by Dissipation in Atomic Quantum Wires
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Biorthogonal Quantum Mechanics
• Edge states and topological phases in non-Hermitian systems
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Topological Transition in a Non-Hermitian Quantum Walk
• Topologically protected midgap states in complex photonic lattices
• Observation of a dynamical topological phase transition
• New topological invariants in non-Hermitian systems
• Equilibration and Order in Quantum Floquet Matter
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Dynamical Topological Order Parameters far from Equilibrium
• Topological invariance and global Berry phase in non-Hermitian systems
• Dynamical quantum phase transitions: scaling and universality
• Topological classification of dynamical phase transitions
• Simulating dynamic quantum phase transitions in photonic quantum walks
• Detecting topological invariants in nonunitary discrete-time quantum walks
• Dynamical preparation of Floquet Chern insulators
• Measuring topology by dynamics: Chern number from linking number
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Parity-time-symmetric topological superconductor
• Measuring Topological Number of a Chern-Insulator from Quench Dynamics
• Quantum Quenches in Chern Insulators
• Observation of symmetry-protected topological band with ultracold fermions
• Dynamical classification of topological quantum phases
• Dynamical quantum phase transitions in non-Hermitian lattices
• Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics
• Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps
• Dynamical topological invariant after a quantum quench
• Dynamical Buildup of a Quantized Hall Response from Non-Topological States
• Topological Entanglement-Spectrum Crossing in Quench Dynamics
• Persistent Hall response in a quantum quench
• Dynamical detection of topological charges
• Hall Response and Edge Current Dynamics in Chern Insulators out of Equilibrium
• Topology and entanglement in quench dynamics

Cited by in corpus (32)

• Non-Hermitian Physics
• Symmetry and Topology in Non-Hermitian Physics
• Simulating dynamic quantum phase transitions in photonic quantum walks
• Topological Phases in Non-Hermitian Aubry-André-Harper Models
• Observation of emergent momentum-time skyrmions in parity-time-symmetric non-unitary quench dynamics
• Topological quantum walks in momentum space with a Bose-Einstein condensate
• Dynamical detection of topological charges
• Detecting non-Bloch topological invariants in quantum dynamics
• Deconstructing effective non-Hermitian dynamics in quadratic bosonic Hamiltonians
• Dynamic winding number for exploring band topology
• Dynamics of entanglement after exceptional quantum quench
• Non-Bloch quench dynamics
• Topological holographic quench dynamics in a synthetic dimension
• Dynamical scaling of Loschmidt echo in non-Hermitian systems
• Universal topological quench dynamics: Altland-Zirnbauer tenfold classes
• Emergent topology under slow non-adiabatic quantum dynamics
• Real spectra, Anderson localization, and topological phases in one-dimensional quasireciprocal systems
• Linking invariant for the quench dynamics of a two-dimensional two-band Chern insulator
• Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation
• Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
• Dynamically characterizing topological phases by high-order topological charges
• Anomalous dynamical response of non-Hermitian topological phases
• Dynamics of the Geometric Phase in Inhomogeneous Quantum Spin Chains
• Stability of dynamical topology against dynamical noise in quantum quenches
• Synthetic topology and Floquet dynamic quantum phase transition in a periodically driven Raman lattice
• Generic theory of characterizing topological phases under quantum slow dynamics
• Work statistics and generalized Loschmidt echo for the Hatano-Nelson model
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Dynamic transition of the density-matrix topology under parity-time symmetry
• Dynamical Quantum Phase Transitions and Many-Body Backflow in Open Quantum Systems
• Dissipation-Induced Deviations from Kibble-Zurek Scaling in Non-Hermitian Quantum Annealing
• Full investigation of nonadiabatic dynamical characterization in arbitrary quenching process