Construction of $G_2$ symmetry in a Hubbard-type model
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866913623738155008 |
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| author | Gao, Zhi-Qiang Wu, Congjun |
| author_facet | Gao, Zhi-Qiang Wu, Congjun |
| contents | As the smallest exceptional Lie group and the automorphism group of the non-associative algebra octonions, $G_2$ is often employed for describing exotic symmetry structures. We construct $G_2$ 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 $G_2$ symmetry can be spontaneously broken into either an $SU(3)$ one associated with an $S^6$ sphere Goldstone manifold, or, into $SU(2)\times U(1)$ with a Grassmannian Goldstone manifold. In the quantum disordered states, quantum fluctuations generate the effective $SU(3)$ and $SU(2)\times U(1)$ gauge theories for low energy fermions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_14126 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Construction of $G_2$ symmetry in a Hubbard-type model Gao, Zhi-Qiang Wu, Congjun Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory As the smallest exceptional Lie group and the automorphism group of the non-associative algebra octonions, $G_2$ is often employed for describing exotic symmetry structures. We construct $G_2$ 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 $G_2$ symmetry can be spontaneously broken into either an $SU(3)$ one associated with an $S^6$ sphere Goldstone manifold, or, into $SU(2)\times U(1)$ with a Grassmannian Goldstone manifold. In the quantum disordered states, quantum fluctuations generate the effective $SU(3)$ and $SU(2)\times U(1)$ gauge theories for low energy fermions. |
| title | Construction of $G_2$ symmetry in a Hubbard-type model |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2010.14126 |