Quadratic-band-touching Hamiltonians in 2D possess USp(2N) symmetry; respecting interactions are limited to two terms that either preserve the symmetry or break it to USp(N) x USp(N), while lattice versions reduce to U(N) symmetry.
Zee,Group Theory in Nutshell for Physicists, (Princeton University Press, Princeton, 2016)
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Symplectic symmetry of quadratic-band-touching Hamiltonians in two dimensions
Quadratic-band-touching Hamiltonians in 2D possess USp(2N) symmetry; respecting interactions are limited to two terms that either preserve the symmetry or break it to USp(N) x USp(N), while lattice versions reduce to U(N) symmetry.