论文标题
$ g_2 $对称性在哈伯德型模型中
Construction of $G_2$ symmetry in a Hubbard-type model
论文作者
论文摘要
作为非缔合代数八月座的最小特殊谎言组和自动形态群，通常使用$ g_2 $来描述异国情调的对称结构。我们将$ g_2 $对称性构造在一个自动偶像哈伯德型模型中，其中具有4组分费米子在双分晶格中，这在两个$ so（7）$代数的相交中，由Octonions的结构常数连接。根据订单参数的表示形式，$ g_2 $对称性可以自发地分成$ su（3）$一个与$ s^6 $ sphere Goldstone歧管相关的$ SU（2）\ su（2）\ times u（1）$与Grassmannian Goldstone comploct。在量子无序状态下，量子波动产生有效的$ SU（3）$（3）$（2）\ times U（1）$ $级别的低能费用理论。
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.
