Hubbard clusters as testing grounds for noncollinear spins in (TD)DFT

Commonly used DFT approximations for noncollinear magnetism, most notably the LSDA, are based on reference systems with collinear spins; this neglects exchange-correlation (xc) torque effects. In order to test when these xc torques are important it is helpful to have a fully solvable model to compare to DFT approximations. Finite sized Hubbard models are an ideal testing ground for DFT, but the most common systems in use, the dimer and trimer, are too small to model extended Hubbard interactions, which are necessary for non-trivial exchange torques to arise. We advocate for the use of a half-filled 5-site Hubbard cluster in DFT testing of orbital-dependent xc functionals, including spin-orbit coupling induced geometric frustrations. We find that xc torques make a significant contribution to the noncollinear spin dynamics, especially in the vicinity of boundaries between different phases of frustration.