  We study the magnetic phase diagram of spin-3/2 fermions in a spatially
anisotropic square optical lattice at quarter filling (corresponding to one
particle per lattice site). In the limit of the large on-site repulsion the
system can be mapped to the so-called Sp(N) Heisenberg spin model with N=4. We
analyze the Sp(N) spin model with the help of the large-N field-theoretical
approach and show that the effective theory corresponds to the Sp(N) extension
of the CP^{N-1} model, with the Lorentz invariance generically broken. We
obtain the renormalization flow of the model couplings and show that although
the Sp(N) terms are seemingly irrelevant, their presence leads to a
renormalization of the CP^{N-1} part of the action, driving a phase transition.
We further consider the influence of the external magnetic field (the quadratic
Zeeman effect), and present the qualitative analysis of the ground state phase
diagram.
