Antiferromagnetic chiral spin density wave and strain-induced Chern insulator in the square lattice Hubbard model with frustration

We employ the Hartree-Fock approximation to identify the magnetic ground state of the Hubbard model on a frustrated square lattice. We investigate the phase diagram as a function of the Coulomb repulsions strength $U$, and the ratio $t/t$ between the nearest and next nearest neighbor hoppings $t$ and $t$. At half-filling and for a sufficiently large $U$, an antiferromagnetic chiral spin density wave order with nonzero spin chirality emerges as the ground state in a wide regime of the phase diagram near $t/t=1/sqrt{2}$, where the Fermi surface is well-nested for both $(pi,pi)$ and $(pi,0)/(0,pi)$ wave vectors. This triple-${bf Q}$ chiral phase is sandwiched by a single-${bf Q}$ N{e}el phase and a double-${bf Q}$ coplanar spin-vortex crystal phase, at smaller and larger $t/t$, respectively. The energy spectrum in the chiral spin density wave phase consists of four pairs of degenerate bands. These give rise to two pairs of Dirac cones with the same chirality at the point $({pi over 2},{piover 2})$ of the Brillouin zone. We demonstrate that the application of a diagonal strain induces a $d_{xy}$-wave next nearest neighbor hopping which, in turn, opens gaps in the two Dirac cones with opposite masses. As a result, four pairs of well-separated topologically-nontrivial bands emerge, and each pair of those contributes with a Chern number $pm1$. At half-filling, this leads to a zero total Chern number and renders the topologically-notrivial properties observable only in the ac response regime. Instead, we show that at $3/4$ filling, the triple-${bf Q}$ chiral phase yields a Chern insulator exhibiting the quantum anomalous Hall effect.