  Sr2IrO4 has been suggested as a Mott insulator from a single J_eff=1/2 band,
similar to the cuprates. However this picture is complicated by the measured
large magnetic anisotropy and ferromagnetism. Based on a careful mapping to the
J_eff=1/2 (pseudospin-1/2) space, we propose that the low energy electronic
structure of Sr2IrO4 can indeed be described by a SU(2) invariant
pseudospin-1/2 Hubbard model very similar to that of the cuprates, but with a
"twisted" coupling to external magnetic field (a g-tensor with a staggered
antisymmetric component). This perspective naturally explains the magnetic
properties of Sr2IrO4. We also derive several simple facts based on this
mapping and the known results about the Hubbard model and the cuprates, which
may be tested in future experiments on Sr2IrO4. In particular we propose that
(electron-)doping Sr2IrO4 can potentially realize high-temperature
superconductivity.
