Driven Hubbard model on a triangular lattice: Tunable Heisenberg antiferromagnetwith a chiral three-spin term

We study the effect of a periodically varying electric field on the Hubbard model at half filling on a triangular

lattice. The electric field is incorporated through the phase of the nearest-neighbor hopping amplitude via the

Peierls prescription. When the on-site interaction is much larger than the hopping, 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

breaks 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. 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 ground state

phase diagram with seven different phases consisting of two kinds of ordered phases (collinear and coplanar) and

disordered phases. Thus periodic driving of the Hubbard model on a triangular lattice can lead to an effective spin

model whose couplings can be tuned over a range of values thus producing a variety of interesting phases.

Reference:

S. Sur, A. Udupa and D. Sen, Phys. Rev. B 105, 054423 (2022).