Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators
By T. Mikami, Sota Kitamura, K. Yasuda, N. Tsuji, T. Oka, H. Aoki. 2015
243 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/c918e7548b5c8848d210ae1e7e3864b5e9334396
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Artificial gauge fields in materials and engineered systems (2017, unknown): “The effective Hamiltonian Heff can be computed from the operators H0 and V (t), using an inverse-frequency perturbative expansion [55,59,56,60,61], namely, assuming a high-frequency limit ω = 2π/T → ∞.”
- Topological photonics (2018, background): “(30), can be systematically computed using various perturbative treatments (Goldman and Dalibard, 2014; Bukov, D’Alessio, and Polkovnikov, 2015; Eckardt and Anisimovas, 2015; Goldman et al., 2015; Mikami et al., 2016).”
- Colloquium: Nonthermal pathways to ultrafast control in quantum materials (2021, background): “10(b)], with the difference being that the multitude of Floquet-Bloch bands that form due to the additional gap openings can have Chern numbers jCj > 1, i.e., multiple edge modes (Usaj et al., 2014; Dehghani, Oka, and Mitra, 2015; Sentef et al., 2015; Claassen et al., 2016; Mikami et al., 2016).”