Quaternionic Berry connection by the Kramers multiplet and physical applications

最近，Hatsugai提出了具有时间反转对称性的Kramers多重子的Berry连接理论。目前的项目是发展这一萌芽研究领域，并追求使用四元数Berry连接来定义拓扑顺序参数。将其基本思想应用于具有Sp(1)规范对称的焦绿石/Kagome晶格系统，作为任意维度的一系列模型。进一步阐明了它们的拓扑特征。

Recently a theory of the Berry connection of the Kramers multiplet with the time-reversal symmetry is formulated by Hatsugai. The present project is to develop this embryonic research area and to pursue the use of quaternionic Berry connections to define topological order parameters. The basic idea is applied for pyrochlore/Kagome lattice systems with Sp(1) gauge symmetry as a series of models in any dimensions. Further their topological characters are clarified.