TY - JOUR
T1 - Topological phase transitions in finite-size periodically driven translationally invariant systems
AU - Ge, Yang
AU - Rigol, Marcos
N1 - Funding Information:
This work was supported by the Office of Naval Research, Grant No. N00014-14-1-0540. The computations were done at the Institute for CyberScience at Penn State.
Publisher Copyright:
© 2017 American Physical Society.
PY - 2017/8/9
Y1 - 2017/8/9
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevA.96.023610
DO - 10.1103/PhysRevA.96.023610
M3 - Article
AN - SCOPUS:85028650906
VL - 96
JO - Physical Review A
JF - Physical Review A
SN - 2469-9926
IS - 2
M1 - 023610
ER -