论文标题
来自对称性的Uhlmann仪表组的干涉测量几何形状与拓扑相变的应用
Interferometric geometry from symmetry-broken Uhlmann gauge group with applications to topological phase transitions
论文作者
论文摘要
我们提供了Riemannian结构的自然概括，即Sjöqvist最近引入的指标，用于非退化密度矩阵的空间，以变性的情况，即特征面积具有大于或等于1的情况。我们对计量的物理解释进行了分解测量。我们将这种标准应用于物理解释为干涉敏感性，用于研究带绝缘子在有限温度下的拓扑相变。我们比较了这种敏感性的行为，以及来自众所周知的Bures指标的行为，表明它们在很大程度上不同。尽管两者都推断零温度相变过，但只有前者也可以预测有限温度相变。行为的差异可以追溯到类似于Landau-Ginzburg理论的对称性破坏机制，通过该理论，Uhlmann量规组被分解为由系统密度矩阵的类型（即光谱投影仪的等级）确定的子组。
We provide a natural generalization of a Riemannian structure, i.e., a metric, recently introduced by Sjöqvist for the space of non degenerate density matrices, to the degenerate case, i.e., the case in which the eigenspaces have dimension greater than or equal to 1. We present a physical interpretation of the metric in terms of an interferometric measurement. We apply this metric, physically interpreted as an interferometric susceptibility, to the study of topological phase transitions at finite temperatures for band insulators. We compare the behaviors of this susceptibility and the one coming from the well-known Bures metric, showing them to be dramatically different. While both infer zero temperature phase transitions, only the former predicts finite temperature phase transitions as well. The difference in behaviors can be traced back to a symmetry breaking mechanism, akin to Landau-Ginzburg theory, by which the Uhlmann gauge group is broken down to a subgroup determined by the type of the system's density matrix (i.e., the ranks of its spectral projectors).
