Hidden $\mathrm{SU(4)}$ symmetry in bilayer quantum well at integer filling factors

Phase diagram of a bilayer quantum well at integer filling factors is established using the hidden symmetry method. Three phases: ferromagnetic, canted antiferromagnetic (CAP) and spin-singlet, have been found. We confirm early results of Das Sarma et al. Each phase violates the $\mathrm{SU(4)}$ hidden symmetry and is stabilized by the anisotropy interactions.