Testing of two-dimensional local approximations in the current-spin and spin-density-functional theories

We study a model quantum dot system in an external magnetic field by using both spin-density-functional theory and current-spin density-functional theory. The theories are used with local approximations for the spin-density and vorticity. The reliabilities of different parametrizations for the exchange-correlation functionals are tested by comparing the ensuing energetics with quantum Monte Carlo results. The limit where the vorticity dependence should be used in the exchange-correlation functionals is discussed.