  We use the bilayer twisted Hubbard model to study the low energy electronic
structure of Sr3Ir2O7. Sr3Ir2O7 is suggested as a Mott insulator and described
by the bilayer twisted pseudospin-1/2 model. The bilayer twists in Sr3Ir2O7
bring the intrinsic anisotropy and the system is no longer SU(2) invariant. The
anisotropy selects an easy c-axis collinear antiferromagnetic magnetic
structure at low temperatures which breaks the discrete Ising symmetry. The
transverse spin excitations are gapped and the longitudinal one is weakly
dispersive. We implement the bond-operator mean field calculation to describe
the magnetic properties of the bilayer twisted pseudospin-1/2 model in good
agreement with experimental measurements in Sr3Ir2O7. The bilayer twisted
Hubbard model is believed to be the good zeroth approximation for the low
energy electronic structure of Sr3Ir2O7.
