Density-functional theory for noncollinear magnetism: exact and approximate results on small Hubbard chains

We apply a class of orbital-dependent exchange-correlation functionals (exact exchange and Singwi-Tosi-Land-Sjolander exchange-correlation) to two-electron systems on small Hubbard chains in the presence of noncollinear magnetic fields. We compare these approximations with benchmark results obtained from exact diagonalization and inversion of the Kohn-Sham equation via a conjugate-gradient optimization. In general, good agreement is found for total energies, densities and magnetizations over a range of interaction strengths. Exchange-correlation torques, on the other hand, are more subtle and can be difficult to approximate, especially for strong correlations.