Topology and entanglement in quench dynamics

TL;DR

This paper classifies the topology of quench dynamics using homotopy groups, linking topological invariants of post-quench states to static Hamiltonians, and reveals how entanglement spectra reflect these topological features across different dimensions.

Contribution

It introduces a classification scheme for quench dynamics topology via homotopy groups and relates entanglement spectrum features to topological invariants in various dimensions.

Findings

Mid-gap entanglement spectrum states form rings in 2D Chern insulators.

Number of Dirac cones equals the second Chern number in 3+1D.

Topological invariants of post-quench states relate to static Hamiltonian invariants.

Abstract

We classify the topology of quench dynamics by homotopy groups. A relation between the topological invariant of a post-quench order parameter and the topological invariant of a static Hamiltonian is shown in one, two and three dimensions. The mid-gap states in the entanglement spectrum of the post-quench state reveal its topological nature. When a trivial quantum state under a sudden quench to a Chern insulator, the mid-gap states in entanglement spectrum form rings. These rings are analogous to the boundary Fermi rings in the Hopf insulators. Finally, we show a post-quench state in 3+1 dimensions can be characterized by the second Chern number. The number of Dirac cones in the entanglement spectrum is equal to the second Chern number.