基于Uhlmann相的开放系统和热系统的拓扑指数
Topological indices for open and thermal systems via Uhlmann's phase
摘要：
二维拓扑相位由TKNN整数表征，其对布洛赫能带或布洛赫带群进行分类。然而，量子化不能存活热平均或移相到混合状态。我们表明，使用Uhlmann的平行运输密度矩阵（Rep. Math. Phys. 24，229（1986）），拓扑相位的整数分类可以定义为一个有限的广义温度$T$或移相Lindbladian。该方案减少到熟悉的TKNN分类为$T<T_{{\rm c},1}$，成为平凡的$T>T_{{\rm c},2}$，并表现出一个“无间隙”的中间制度，拓扑指数没有很好地定义。我们详细地展示了这些想法，将它们应用于Haldinger的蜂窝晶格模型和Bernevig-Hughes-Zhang模型，并评论了它们对多频带陈省身绝缘体的推广。
英文摘要：
Two-dimensional topological phases are characterized by TKNN integers, which classify Bloch energy bands or groups of Bloch bands. However, quantization does not survive thermal averaging or dephasing to mixed states. We show that using Uhlmann's parallel transport for density matrices (Rep. Math. Phys. 24, 229 (1986)), an integer classification of topological phases can be defined for a finite generalized temperature $T$ or dephasing Lindbladian. This scheme reduces to the familiar TKNN classification for $T<T_{{\rm c},1}$, becomes trivial for $T>T_{{\rm c},2}$, and exhibits a `gapless' intermediate regime where topological indices are not well-defined. We demonstrate these ideas in detail, applying them to Haldane's honeycomb lattice model and the Bernevig-Hughes-Zhang model, and we comment on their generalization to multi-band Chern insulators.
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