论文标题
$ O（n）$ fermionic链的最低能量状态
Lowest energy states of an $O(N)$ fermionic chain
论文作者
论文摘要
考虑到具有$ n $内部自由度（口味）和$ o（n）$对称性的一般有限大小的费米子链。在自由边界条件的情况下，我们证明具有恰好具有$ m $ M $粒子数字的不变扇区中的基态由单个等级$ m $反对称的多重组表示。对于均匀的链条，其粒子孔量子数（如果是一个好的量子）由$ M $的奇偶校验给出。对于奇数链，粒子对称性会导致共轭多重组之间的双性变性。对于反对称表示的$ O（n）$混合旋转链也证明了类似的陈述。结果扩展到远程相互作用的费米子，（部分）到翻译不变链。
A quite general finite-size chain of fermions with $N$ internal degrees of freedom (flavors) and $O(N)$ symmetry is considered. In the case of the free boundary condition, we prove that the ground state in the invariant sector having exactly $m$ flavors with an odd particle number is represented by a single rank-$m$ antisymmetric multiplet. For the even-length chains, its particle-hole quantum number (if it's a good one) is given by the parity of the $m$. For the odd-length chains, the particle-hole symmetry leads to the twofold degeneracy among the conjugate multiplets. Similar statements are proven for the $O(N)$ mixed-spin chains in antisymmetric representations. The results are extended to the long-range interacting fermions and (partially) to the translation invariant chains.
