Topological phase transitions in finite-size periodically driven translationally invariant systems

Yang Ge, Marcos Rigol

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish (US)
Article number023610
JournalPhysical Review A
Issue number2
StatePublished - Aug 9 2017

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


Dive into the research topics of 'Topological phase transitions in finite-size periodically driven translationally invariant systems'. Together they form a unique fingerprint.

Cite this