Uhlmann phase of coherent states and the Uhlmann-Berry correspondence
Uhlmann phase of coherent states and the Uhlmann-Berry correspondence
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DOI：
10.21468/scipostphyscore.6.1.024
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发表时间：
2022-08
影响因子：
3.6
通讯作者：
Xin Wang;Xu-Yang Hou;Zhengui Zhou;Hao Guo;C. Chien
中科院分区：
文献类型：
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作者：
Xin Wang;Xu-Yang Hou;Zhengui Zhou;Hao Guo;C. Chien
我们首先比较了光纤束语言中乌尔曼相和贝里相背后的几何框架，然后评估了玻色子和费米子相干态的乌尔曼相。两种相干态的乌尔曼相均携带几何信息，且随温度的升高而平滑减小。重要的是，随着温度的降低，乌尔曼相接近于相应的贝里相。结合以往文献中的例子，我们提出了乌尔曼相和贝里相在零温度极限下的对应关系，作为除一些特殊情况外的一般性质，并给出了这种对应关系的条件证明。
We first compare the geometric frameworks behind the Uhlmann and Berry phases in a fiber-bundle language and then evaluate the Uhlmann phases of bosonic and fermionic coherent states. The Uhlmann phases of both coherent states are shown to carry geometric information and decrease smoothly with temperature. Importantly, the Uhlmann phases approach the corresponding Berry phases as temperature decreases. Together with previous examples in the literature, we propose a correspondence between the Uhlmann and Berry phases in the zero-temperature limit as a general property except some special cases and present a conditional proof of the correspondence.