2017/06/30 by Yang Ge, Ge Yang, Marcos Rigol · 22 citations
Mathematics · Physics and Astronomy · #Boundary value problem #Brillouin zone #Chern class #Cold Atom Physics and Bose-Einstein Condensates #Invariant (physics) #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Periodic boundary conditions #Phase space #Phase transition #Physics #Position and momentum space #Pure mathematics #Quantum many-body systems #Quantum mechanics #Thermodynamic limit #Topological Materials and Phenomena #Topological index #Topology (electrical circuits) #Unitary state #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.96.023610
published in Physical Review A 96(2) (American Physical Society) · 8 pages, 4 figures. Updated to published version with the addition of Ref [32]. Typo fix
openalex created_date 2017/06/23 · openalex publication_date 2017/08/09 · arxiv created 2018/04/28 · arxiv updated 2018/05/01 · openalex updated_date 2026/08/05
It is known that, in the thermodynamic limit, the Chern number of a translationally invariant system cannot change under unitary time evolutions that are smooth in momentum space. Yet a real-space counterpart of the Chern number, the Bott index, has been shown to change in periodically driven systems with open boundary conditions. Here we prove that the Bott index and the Chern number are identical in translationally invariant systems in the thermodynamic limit. Using the Bott index, we show that, in finite-size translationally invariant systems, a Fermi sea under a periodic drive that is turned on slowly can acquire a different topology from that of the initial state. This can happen provided that the gap-closing points in the thermodynamic limit are absent in the discrete Brillouin zone of the finite system. Hence, in such systems, a periodic drive can be used to dynamically prepare topologically nontrivial states starting from topologically trivial ones.