Topological quantum quench dynamics carrying arbitrary Hopf and second-Chern numbers

Abstract

A quantum quench is a nonequilibrium dynamics governed by the unitary evolution. We propose a two-band model whose quench dynamics is characterized by an arbitrary Hopf number belonging to the homotopy group ${\pi }_3(S^2)=\mathbb{Z}$. When we quench a system from an insulator with the Chern number $C_i\in {\pi }_2(S^2)=\mathbb{Z}$ to another insulator with the Chern number $C_f$, the preimage of the Hamiltonian vector forms links having the Hopf number $C_f-C_i$. We also investigate a quantum-quench dynamics for a four-band model carrying an arbitrary second-Chern number $N\in {\pi }_4(S^4)=\mathbb{Z}$, which can be realized by quenching a three-dimensional topological insulator having the three-dimensional winding number $N\in {\pi }_3(S^3)=\mathbb{Z}$.

arXiv comment6 pages, 5 figures

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Cited by in corpus (9)

• Topological Invariants for Quantum Quench Dynamics from Unitary Evolution
• Nonanalyticity of circuit complexity across topological phase transitions
• Measuring Hopf links and Hopf invariants in a quenched topological Raman lattice
• Linking invariant for the quench dynamics of a two-dimensional two-band Chern insulator
• Out of equilibrium chiral higher order topological insulator on a $\pi$-flux square lattice
• Quantum quenches in a pseudo-Hermitian Chern insulator
• Second Euler number in four dimensional synthetic matter
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• From orthogonal link to phase vortex in generalized dynamical Hopf insulators