Phase vortices of the quenched Haldane Model

Abstract

Using the recently developed Bloch-state tomography technique, the quasimomentum $\mathbf{k}$-dependent Bloch states ${\left(\sin \left({\theta }_{\mathbf{k}}/2\right),-\cos \left({\theta }_{\mathbf{k}}/2\right)e^{i{\varphi }_{\mathbf{k}}}\right)}^T$ of a two-band tight-binding model with two sublattices can be mapped out. We show that, if we prepare the initial Bloch state as the lower-band eigenstate of a topologically trivial Haldane Hamiltonian $H_i$, and then quench the Haldane Hamiltonian to $H_f$, the time-dependent azimuthal phase ${\varphi }_{\mathbf{k}}(t)$ supports two types of vortices. The first type of vortices are static, with the corresponding Bloch vectors pointing to the north pole (${\theta }_{\mathbf{k}}=0$). The second type of vortices are dynamical, with the corresponding Bloch vectors pointing to the south pole (${\theta }_{\mathbf{k}}=\pi$). In the $(k_x,k_y,t)$ space, the linking number between the trajectories of these two types of vortices equals exactly to the Chern number of the lower band of $H_f$, which provides an alternative method to directly map out the topological phase boundaries of the Haldane model.

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Cited by in corpus (20)

• Observation of a dynamical topological phase transition
• Measuring topology by dynamics: Chern number from linking number
• Dynamical topological invariant after a quantum quench
• Hopf characterization of two-dimensional Floquet topological insulators
• Topological Invariants for Quantum Quench Dynamics from Unitary Evolution
• Extracting the Quantum Geometric Tensor of an Optical Raman Lattice by Bloch State Tomography
• Dynamical topological invariants and reduced rate functions for dynamical quantum phase transitions in two dimensions
• Nonanalyticity of circuit complexity across topological phase transitions
• Topologically induced prescrambling and dynamical detection of topological phase transitions at infinite temperature
• Measuring Hopf links and Hopf invariants in a quenched topological Raman lattice
• Quench dynamics and scaling laws in topological nodal loop semimetals
• Dynamical quantum phase transitions in Weyl semimetals
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• Stability of entanglement-spectrum crossing in quench dynamics of one dimensional gapped free-fermion systems
• Quench dynamics of Hopf insulators
• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Vortex loop dynamics and dynamical quantum phase transitions in 3D fermion matter
• Few-particle dynamics of fractional quantum Hall lattice models
• Dynamical signatures of symmetry protected topology following symmetry breaking
• From orthogonal link to phase vortex in generalized dynamical Hopf insulators