Quench dynamics of Hopf insulators

Abstract

Hopf insulators are exotic topological states of matter outside the standard ten-fold way classification based on discrete symmetries. Its topology is captured by an integer invariant that describes the linking structures of the Hamiltonian in the three-dimensional momentum space. In this paper, we investigate the quantum dynamics of Hopf insulators across a sudden quench and show that the quench dynamics is characterized by a ${\mathbb{Z}}_2$ invariant $\nu$ which reveals a rich interplay between quantum quench and static band topology. We construct the ${\mathbb{Z}}_2$ topological invariant using the loop unitary operator, and prove that $\nu$ relates the pre- and post-quench Hopf invariants through $\nu =(\mathcal{L}-{\mathcal{L}}_0)\mathrm{mod}2$. The ${\mathbb{Z}}_2$ nature of the dynamical invariant is in sharp contrast to the $\mathbb{Z}$ invariant for the quench dynamics of Chern insulators in two dimensions. The non-trivial dynamical topology is further attributed to the emergence of $\pi$-defects in the phase band of the loop unitary. These $\pi$-defects are generally closed curves in the momentum-time space, for example, as nodal rings carrying Hopf charge.

arXiv comment10 pages, 5 figures

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Cited by in corpus (7)

• Topological Invariants for Quantum Quench Dynamics from Unitary Evolution
• Realizing Hopf Insulators in Dipolar Spin Systems
• Floquet Engineering Ultracold Polar Molecules to Simulate Topological Insulators
• Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation
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• Tuning the topology of $p$-wave superconductivity in an analytically solvable two-band model
• Loop unitary and phase band topological invariant in generic multi-band Chern insulators