Dynamical Geometry of the Haldane Model under a Quantum Quench

Abstract

We explore the time evolution of a topological system when the system undergoes a sudden quantum quench within the same nontrivial phase. Using Haldane's honeycomb model as an example, we show that equilibrium states in a topological phase can be distinguished by geometrical features, such as the characteristic momentum at which the half-occupied edge modes cross, the associated edge-mode velocity, and the winding vector about which the normalized pseudospin magnetic field winds along a great circle on the Bloch sphere. We generalize these geometrical quantities for non-equilibrium states and use them to visualize the quench dynamics of the topological system. In general, we find the pre-quench equilibrium state relaxes to the post-quench equilibrium state in an oscillatory fashion, whose amplitude decay as $t^{1/2}$. In the process, however, the characteristic winding vector of the non-equilibrium system can evolve to regimes that are not reachable with equilibrium states.

13 pages, 11 figures

References in corpus (47)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Evolution of Entanglement Entropy in One-Dimensional Systems
• Time-dependence of correlation functions following a quantum quench
• Calculation of reduced density matrices from correlation functions
• Equilibrium states of generic quantum systems subject to periodic driving
• The Zak phase and the existence of edge states in graphene
• Quantum Many-Body Scars and Weak Breaking of Ergodicity
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Entanglement spectrum of topological insulators and superconductors
• Geometrical Description of the Fractional Quantum Hall Effect
• Real time confinement following a quantum quench to a non-integrable model
• Entanglement spectrum and boundary theories with projected entangled-pair states
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Density-Matrix Spectra of Solvable Fermionic Systems
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Measuring topology by dynamics: Chern number from linking number
• Bulk-Edge Correspondence in the Entanglement Spectra
• Uncover Topology by Quantum Quench Dynamics
• Measuring Topological Number of a Chern-Insulator from Quench Dynamics
• Non-local order in gapless systems: Entanglement Spectrum in Spin Chains
• A geometric proof of the equality between entanglement and edge spectra
• Real-Space Entanglement Spectrum of Quantum Hall States
• Real-space entanglement spectrum of quantum Hall systems
• Model anisotropic quantum Hall states
• Entanglement Oscillations near a Quantum Critical Point
• Topological Entanglement-Spectrum Crossing in Quench Dynamics
• Measurement of the entanglement spectrum of a symmetry-protected topological state using the IBM quantum computer
• Entanglement spectrum and Wannier center flow of the Hofstadter problem
• Dirac points emerging from flat bands in Lieb-kagomé lattices
• Winding vector: how to annihilate two Dirac points with the same charge
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
• Quench dynamics of collective modes in fractional quantum Hall bilayers
• Non-equilibrium Fractional Hall Response After a Topological Quench
• Topology and entanglement in quench dynamics
• Many-particle dephasing after a quench
• Entanglement Spectrum of Composite Fermion States in Real Space
• Polarization and entanglement spectrum in non-hermitian systems
• Dynamical crossover behavior in the relaxation of quenched quantum many-body systems
• Quench dynamics and scaling laws in topological nodal loop semimetals
• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Persistent oscillations after quantum quenches in $d$ dimensions
• Stability of entanglement-spectrum crossing in quench dynamics of one dimensional gapped free-fermion systems
• Power-law decay of correlations after a global quench in the massive XXZ chain
• Decay of long-lived oscillations after quantum quenches in gapped interacting quantum systems
• Dynamical relaxation behavior of extended XY chain with gapless phase following a quantum quench