Symplectic symmetry of quadratic-band-touching Hamiltonians in two dimensions semimetals

Synopsis

The phase transitions in condensed matter systems involve the spontaneous breaking of specific symmetries. The 2 spatial dimensional quadratic band touching (QBT) systems are discovered to exhibit the unitary symplectic symmetry in the Majorana basis. Under the newly discovered unitary symplectic symmetry, all the fermionic bilinears can be classified as the three small irreducible representations (USp(2N) generators, effective masses, and nematics) of this group. The minimal interactive model respecting USp(2N) symmetry is constructed with two independent quartic terms. Under the infrared-relevant limit, the symplectic symmetry either remains preserved or becomes spontaneously broken to USp(N) × USp(N) with the potential to be a new universal class for QBT systems. An additional result of the exact symmetry in the lattices, such as honeycomb or the Bernalstacked bilayer graphene to the infinite order in the dispersion’s expansion in powers of local momentum is given by the intersection of the symplectic and the orthogonal groups, which is O(2N)⋂︁ USp(2N) = U(N).

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