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We employ the Hartree-Fock approximation to identify the magnetic groundstate of the Hubbard model on a frustrated square lattice. We investigate thephase diagram as a function of the Coulomb repulsion's strength $U$, and theratio $t'/t$ between the nearest and next nearest neighbor hoppings $t$ and$t'$. At half-filling and for a sufficiently large $U$, an antiferromagneticchiral spin density wave order with nonzero spin chirality emerges as theground 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 issandwiched by a single-${\bf Q}$ N\'{e}el phase and a double-${\bf Q}$ coplanarspin-vortex crystal phase, at smaller and larger $t'/t$, respectively. Theenergy spectrum in the chiral spin density wave phase consists of four pairs ofdegenerate bands. These give rise to two pairs of Dirac cones with the samechirality at the point $({\pi \over 2},{\pi\over 2})$ of the Brillouin zone. Wedemonstrate that the application of a diagonal strain induces a $d_{xy}$-wavenext nearest neighbor hopping which, in turn, opens gaps in the two Dirac coneswith opposite masses. As a result, four pairs of well-separatedtopologically-nontrivial bands emerge, and each pair of those contributes witha Chern number $\pm1$. At half-filling, this leads to a zero total Chern numberand renders the topologically-notrivial properties observable only in the acresponse regime. Instead, we show that at $3/4$ filling, the triple-${\bf Q}$chiral phase yields a Chern insulator exhibiting the quantum anomalous Halleffect.

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