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Uhlmann phase of coherent states and the Uhlmann-Berry correspondence

Xin WangXu-Yang HouZheng ZhouHao GuoChih-Chun Chien
Aug 2022
摘要
To clarify how the Uhlmann phase generalize the Berry phase of pure states tomixed states, we first compare the geometric frameworks behind the two phasesin a fiber-bundle language. We then apply the frameworks to evaluate theUhlmann phases of bosonic and fermionic coherent states, both of which arebuilding blocks of path integrals in quantum field theory. The Uhlmann phasesof both types of coherent state are shown to carry geometric information anddecrease smoothly with temperature. Importantly, the Uhlmann phases approachthe corresponding Berry phases in both cases as temperature decreases. Togetherwith previous examples in the literature, we propose the correspondence betweenthe Uhlmann and Berry phases in the zero-temperature limit as a generalproperty except those special cases with a 1D Hilbert space. Finally, wepresent a conditional proof of the correspondence.
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