相变费米子系统中的Uhlmann联系
The Uhlmann connection in fermionic systems undergoing phase transitions
摘要：
我们研究了费米子系统中的Uhlmann连接的行为，这些费米子系统经历了相变。特别是，我们分析了一些典型的情况下，拓扑绝缘体和超导体在一维，以及BCS理论的超导性在三维。我们表明，乌尔曼连接信号的相变中的本征基的系统的状态的变化。此外，使用已建立的保真度方法和边缘状态的研究，我们显示的情况下，拓扑绝缘体和超导体的热驱动相变的情况下。我们澄清了什么是相关的参数空间与乌尔曼连接，使它的信号存在的顺序在混合状态。
英文摘要：
We study the behaviour of the Uhlmann connection in systems of fermions undergoing phase transitions. In particular, we analyse some of the paradigmatic cases of topological insulators and superconductors in dimension one, as well as the BCS theory of superconductivity in three dimensions. We show that the Uhlmann connection signals phase transitions in which the eigenbasis of the state of the system changes. Moreover, using the established fidelity approach and the study of the edge states, we show the absence of thermally driven phase transitions in the case of topological insulators and superconductors. We clarify what is the relevant parameter space associated with the Uhlmann connection so that it signals the existence of order in mixed states.
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