标题： 乌尔曼和退化量子系统的纯量威尔泽克-泽相位 显示英文标题

标题： Uhlmann and scalar Wilczek-Zee phases of degenerate quantum systems

摘要： Wilczek-Zee（WZ）规范联络出现在简并态中，而Uhlmann规范联络表征有限温度下的拓扑性质。 我们在一个具有两个双重简并子空间的四能级模型中研究了Uhlmann相位与标量WZ相位之间的可能关系，这些相位分别反映了Uhlmann和WZ规范联络。 通过精确解，我们对比了Uhlmann和WZ联络及其相关相位的行为。 在零温极限下，由于底层拓扑结构，Uhlmann相位可能与简并基态的标量WZ相位一致或不一致。 在解析分析中推导出了一些条件，这些条件下零温极限下的Uhlmann相位收敛于标量WZ相位。 我们还简要讨论了这些现象的可能实现或模拟及其意义。 显示英文摘要

摘要： The Wilczek-Zee (WZ) holonomy arises in degenerate states while the Uhlmann holonomy characterizes finite-temperature topology. We investigate possible relationships between the Uhlmann phase and the scalar WZ phase, which reflects the Uhlmann and WZ holonomy respectively, in an exemplary four-level model with two doubly degenerate subspaces. Through exactly solutions, we contrast the behavior of the Uhlmann and WZ connections and their associated phases. In the zero-temperature limit, the Uhlmann phase may or may not agree with the scalar WZ phase of the degenerate ground states due to the underlying topology. Some conditions are derived in an analytic analysis, under which the Uhlmann phase in the zero-temperature limit converges to the scalar WZ phase. We also briefly discuss possible realizations or simulations of the phenomena as well as their implications.