Testing density functional theory in a quantum Ising chain

By using the quantum Ising chain as a test bed and treating spin polarization along external transverse field "generalized density", we examine performance of different levels density functional approximations parallel to those widely used for interacting electrons, such local approximation (LDA) generalized gradient (GGA). We show that by adding lowest-order nearest-neighbor variation correction simple LDA, semi-local energy in spirit GGA is almost exact over wide range inhomogeneous distribution. In addition, LDA error structures bear high level resemblance phase diagram system. These results provide insights into triumph failure these general context.