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arXiv · 1804.10625

Topology and entanglement in quench dynamics

Po-Yao Chang
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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.

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Po-Yao Chang. 2018-05-27. Topology and entanglement in quench dynamics. https://doi.org/10.1103/physrevb.97.224304

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