2020/10/27 by Zhiqiang Gao, Congjun Wu, Gao, Zhi-Qiang +1
Chemistry · Materials Science · Mathematics · #Advanced NMR Techniques and Applications #Magnetism in coordination complexes #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2010.14126
As the smallest exceptional Lie group and the automorphism group of the non-associative algebra octonions, G2 is often employed for describing exotic symmetry structures. We construct G2 symmetry in a self-dual Hubbard-type model with 4-component fermions in a bipartite lattice, which lies in the intersection of two SO(7) algebras connected by the structure constants of octonions. Depending on the representations of the order parameters, the G2 symmetry can be spontaneously broken into either an SU(3) one associated with an S6 sphere Goldstone manifold, or, into SU(2)× U(1) with a Grassmannian Goldstone manifold. In the quantum disordered states, quantum fluctuations generate the effective SU(3) and SU(2)× U(1) gauge theories for low energy fermions.