对称费米投影和Kitaev表：低维物质的拓扑相
Symmetric Fermi projections and Kitaev's table: topological phases of matter in low dimensions
摘要：
我们回顾Kitaev著名的“周期表”的拓扑相的凝聚态，它确定了基态（费米投影）的间隙周期量子系统的连续变形。我们研究家庭的投影依赖于一个周期性的晶体动量和尊重的对称性，其特征的各类拓扑绝缘体。我们的目标是分类这样的家庭在一个系统的，明确的，建设性的方式：我们确定所有对称类的数值指标，并提供算法变形家庭的预测，其指数一致。为了简单起见，我们说明了0-和1-维系统的方法，并恢复Kitaev等人提出的（弱和强）拓扑不变量。
英文摘要：
We review Kitaev's celebrated "periodic table" for topological phases of condensed matter, which identifies ground states (Fermi projections) of gapped periodic quantum systems up to continuous deformations. We study families of projections which depend on a periodic crystal momentum and respect the symmetries that characterize the various classes of topological insulators. Our aim is to classify such families in a systematic, explicit, and constructive way: we identify numerical indices for all symmetry classes and provide algorithms to deform families of projections whose indices agree. Aiming at simplicity, we illustrate the method for 0- and 1-dimensional systems, and recover the (weak and strong) topological invariants proposed by Kitaev and others.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
