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.
Zinn-Justin,Quantum Field Theory and Critical Phe- nomena, (Clarendon Press, Oxford, 2002)
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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.