Scheme to Measure the Topological Number of a Chern Insulator from Quench Dynamics

Physical Review Letters
Ce WangHui Zhai

Abstract

We show how the topological number of a static Hamiltonian can be measured from a dynamical quench process. We focus on a two-band Chern insulator in two dimension, for instance, the Haldane model, whose dynamical process can be described by a mapping from the [k_{x},k_{y},t] space to the Bloch sphere, characterized by the Hopf invariant. Such a mapping has been constructed experimentally by measurements in cold atom systems. We show that, taking any two constant vectors on the Bloch sphere, their inverse images of this mapping are two trajectories in the [k_{x},k_{y},t] space, and the linking number of these two trajectories exactly equals the Chern number of the static Hamiltonian. Applying this result to a recent experiment from the Hamburg group, we show that the linking number of the trajectories of the phase vortices determines the phase boundary of the static Hamiltonian.

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Citations

Mar 8, 2018·Science Advances·Wonjae LeeDavid S Hall
Mar 2, 2018·Science Advances·Bo SongGyu-Boong Jo
Jan 13, 2019·Physical Review Letters·Luis A Peña ArdilaAndré Eckardt
Jan 5, 2019·Physical Review Letters·Wei SunJian-Wei Pan
Jan 25, 2020·Physical Review Letters·S BarbarinoJ C Budich
Apr 17, 2019·Nature Communications·Matthias TarnowskiChristof Weitenberg
Jun 13, 2020·Physical Review Letters·Biao Huang, W Vincent Liu
Aug 17, 2020·Physical Review Letters·F Nur ÜnalRobert-Jan Slager
Sep 20, 2018·Physical Review Letters·Max McGinley, Nigel R Cooper
Jan 5, 2019·Physical Review Letters·Zongping Gong, Masahito Ueda
Jan 1, 2019·Reviews of Modern Physics·N R CooperI B Spielman
May 10, 2020·Physical Review Letters·Haiping Hu, Erhai Zhao
Feb 23, 2020·Physical Review Letters·Dizhou XieBo Yan
Sep 26, 2020·Physical Review Letters·Mingyuan SunHui Zhai
Nov 26, 2019·Physical Review Letters·Chang-Rui YiJian-Wei Pan
Jan 23, 2021·Physical Review Letters·Tomonari MizoguchiYasuhiro Hatsugai
Jul 17, 2021·Physical Review Letters·Thomas SchusterNorman Y Yao
Oct 9, 2021·Light, Science & Applications·Danying YuLuqi Yuan

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