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We study the effects of a periodically varying electric field on the Hubbardmodel at half-filling on a triangular lattice. The electric field isincorporated through the phase of the nearest-neighbor hopping amplitude viathe Peierls prescription. When the on-site interaction $U$ is much larger thanthe hopping, the effective Hamiltonian $H_{eff}$ describing the spin sector canbe 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 threedifferent nearest-neighbor couplings $(J_\alpha,J_\beta,J_\gamma)$ on bondslying along the different directions. Remarkably, when the periodic drivingdoes not have time-reversal symmetry (TRS), $H_{eff}$ is also found to have achiral three-spin interaction in each triangle, with the coefficient $C$ of theinteraction having opposite signs on up- and down-pointing triangles. Thusperiodic driving which breaks TRS can simulate the effect of a perpendicularmagnetic 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 anddirection of the oscillating electric field. We then study the spin model as afunction of these parameters using exact diagonalization and find a rich phasediagram of the ground state with seven different phases consisting of two kindsof ordered phases (colinear and coplanar) and disordered phases. Thus periodicdriving of the Hubbard model on the triangular lattice can lead to an effectivespin model whose couplings can be tuned over a range of values therebyproducing a variety of interesting phases.

Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term