论文标题
通过部分转置用于费米链的非本地订单参数
Non-local order parameters for fermion chains via the partial transpose
论文作者
论文摘要
在过去的二十年中，已经描述了，预测，分类，提出和测量各种各样的拓扑阶段。尽管方法和哲学有一定的统一性，但现象学却大不相同。这项工作涉及最简单的情况：在一个包含反对对称性的对称组$ g $的情况下，一个空间维度的费米子。在这种情况下，可以进行拓扑阶段的完整分类。然而，这些方法在某种程度上缺乏，因为它们通常不允许轻松确定给定系统的类别。本文将提出针对通过反对对称性定义的非本地阶参数参数的建议。它们被证明是在合适的基础状态下是同型不变的。对于矩阵产品状态，提供了对这些不变的解释：特别是对于粒子孔对称，不变式确定真实的分区超级代数$ \ mathbb {d} $，使得债券代数是矩阵代数超过$ \ m m i \ mathbb {d} $。
In the last two decades, a vast variety of topological phases have been described, predicted, classified, proposed, and measured. While there is a certain unity in method and philosophy, the phenomenology differs wildly. This work deals with the simplest such case: fermions in one spatial dimension, in the presence of a symmetry group $G$ which contains anti-unitary symmetries. A complete classification of topological phases, in this case, is available. Nevertheless, these methods are to some extent lacking as they generally do not allow to determine the class of a given system easily. This paper will take up proposals for non-local order parameters defined through anti-unitary symmetries. They are shown to be homotopy invariants on a suitable set of ground states. For matrix product states, an interpretation of these invariants is provided: in particular, for a particle-hole symmetry, the invariant determines a real division super algebra $\mathbb{D}$ such that the bond algebra is a matrix algebra over $\mathbb{D}$.
