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#### Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators

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##### Citation

Mikami, T., Kitamura, S., Yasuda, K., Tsuji, N., Oka, T., & Aoki, H. (2016). Brillouin-Wigner
theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators.*
Physical Review B,* *93*(14): 144307, pp. 1-25. doi:10.1103/PhysRevB.93.144307.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-C5C6-D

##### Abstract

We construct a systematic high-frequency expansion for periodically
driven quantum systems based on the Brillouin-Wigner (BW) perturbation
theory, which generates an effective Hamiltonian on the projected
zero-photon subspace in the Floquet theory, reproducing the
quasienergies and eigenstates of the original Floquet Hamiltonian up to
desired order in 1/omega, with omega being the frequency of the drive.
The advantage of the BW method is that it is not only efficient in
deriving higher-order terms, but even enables us to write down the whole
infinite series expansion, as compared to the van Vleck degenerate
perturbation theory. The expansion is also free from a spurious
dependence on the driving phase, which has been an obstacle in the
Floquet-Magnus expansion. We apply the BW expansion to various models of
noninteracting electrons driven by circularly polarized light. As the
amplitude of the light is increased, the system undergoes a series of
Floquet topological-to-topological phase transitions, whose phase
boundary in the high-frequency regime is well explained by the BW
expansion. As the frequency is lowered, the high-frequency expansion
breaks down at some point due to band touching with nonzero-photon
sectors, where we find numerically even more intricate and richer
Floquet topological phases spring out. We have then analyzed, with the
Floquet dynamical mean-field theory, the effects of electron-electron
interaction and energy dissipation. We have specifically revealed that
phase transitions from Floquet-topological to Mott insulators emerge,
where the phase boundaries can again be captured with the high-frequency
expansion.