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Journal Article

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


Oka,  Takashi
Physics of Quantum Materials, Max Planck Institute for Chemical Physics of Solids, Max Planck Society;

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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
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.