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Description
We study the effects of a periodically varying electric field on the Hubbard model at half-filling on a triangular lattice. The driving electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the Peierls prescription. When $U$ is much larger than the hopping, the system is a Mott insulator and the effective Hamiltonian $H_{eff}$ describing the spin sector can be found using a Floquet perturbation theory. To third order in the hopping, $H_{eff}$ is found to have the form of a Heisenberg antiferromagnet with three different nearest-neighbor couplings $(J_\alpha,J_\beta,J_\gamma)$ on bonds lying along the different directions. Remarkably, when the periodic driving does not have time-reversal symmetry, $H_{eff}$ can also have a chiral three-spin interaction in each triangle, with the coefficient $C$ of the interaction having opposite signs on up- and down-pointing triangles. Thus periodic driving which breaks time-reversal symmetry can simulate the effect of a perpendicular magnetic flux which is known to generate such a chiral term in the spin sector, even though our model does not have a magnetic flux. The four parameters $(J_\alpha,J_\beta,J_\gamma,C)$ depend on the amplitude, frequency and direction of the oscillating electric field. We then study the spin model as a function of these parameters using exact diagonalization and find a rich phase diagram of the ground state with seven different phases consisting of two kinds of ordered phases (collinear and co-planar) and disordered phases. Thus periodic driving of the Hubbard model on the triangular lattice can lead to an effective spin model whose couplings can be tuned over a range of values thereby producing a variety of interesting phases.
Reference: Samudra Sur, Adithi Udupa, and Diptiman Sen, Phys. Rev. B 105, 054423 (2022)
