论文标题
来自SU（$ n $）链的Flag Sigma型号
Flag manifold sigma models from SU($n$) chains
论文作者
论文摘要
在每个站点上考虑了具有相同不可约的表示$ \ Mathcal {r} $的一维SU（$ n $）链。我们确定哪个$ \ MATHCAL {R} $接收到$ \ text {su}（n）/[\ text {u}（1）（1）]^{n-1} $ flag sigma模型，并计算此类理论的拓扑角度。通常，这些模型将具有线性和二次分散关系的字段。对于每个$ \ MATHCAL {R} $，我们确定每个分散类型的字段数量有多少个字段。最后，对于纯线性分散的理论，我们列出了不可减至的表示，该表示还具有$ \ mathbb {z} _n $对称性，该表示在$ \ text {su}（su}（n）/[\ text {u} {u}（u}（u}（u}（u}（1）（1））^n-1]^{n-1} $ fieldss）$ fields。在某些情况下，这种SU（$ n $）连锁店在hhoft异常中有一个hhoft异常，从而可以将Haldane的猜想推广到这些新颖的表现中。特别是，对于$ n $，对于年轻tableaux的表示形式，长度为$ p_1 $和$ p_2 $满足$ p_1 \ not = p_2 $，我们预计当$ p_1+p_2 $是$ n $的cocrime时，我们预计无间隙地面状态。否则，我们预测，如果$ p_1+p_2 $不是$ n $的倍数，那么如果$ n $的倍数，则必须自发损坏对称性。
One dimensional SU($n$) chains with the same irreducible representation $\mathcal{R}$ at each site are considered. We determine which $\mathcal{R}$ admit low-energy mappings to a $\text{SU}(n)/[\text{U}(1)]^{n-1}$ flag manifold sigma model, and calculate the topological angles for such theories. Generically, these models will have fields with both linear and quadratic dispersion relations; for each $\mathcal{R}$, we determine how many fields of each dispersion type there are. Finally, for purely linearly-dispersing theories, we list the irreducible representations that also possess a $\mathbb{Z}_n$ symmetry that acts transitively on the $\text{SU}(n)/[\text{U}(1)]^{n-1}$ fields. Such SU($n$) chains have an 't Hooft anomaly in certain cases, allowing for a generalization of Haldane's conjecture to these novel representations. In particular, for even $n$ and for representations whose Young tableaux have two rows, of lengths $p_1$ and $p_2$ satisfying $p_1\not=p_2$, we predict a gapless ground state when $p_1+p_2$ is coprime with $n$. Otherwise, we predict a gapped ground state that necessarily has spontaneously broken symmetry if $p_1+p_2$ is not a multiple of $n$.
