Schrieffer-Wolff Transformation for periodically driven systems: strongly correlated systems with artificial gauge fields
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Citation (published version)Marin Bukov, Michael Kolodrubetz, Anatoli Polkovnikov. 2016. "Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields." PHYSICAL REVIEW LETTERS, Volume 116, Issue 12, pp. ? - ? (6). https://doi.org/10.1103/PhysRevLett.116.125301
We generalize the Schrieffer-Wolff transformation to periodically driven systems using Floquet theory. The method is applied to the periodically driven, strongly interacting Fermi-Hubbard model, for which we identify two regimes resulting in different effective low-energy Hamiltonians. In the nonresonant regime, we realize an interacting spin model coupled to a static gauge field with a nonzero flux per plaquette. In the resonant regime, where the Hubbard interaction is a multiple of the driving frequency, we derive an effective Hamiltonian featuring doublon association and dissociation processes. The ground state of this Hamiltonian undergoes a phase transition between an ordered phase and a gapless Luttinger liquid phase. One can tune the system between different phases by changing the amplitude of the periodic drive.