Uhlmann phase of coherent states and the Uhlmann-Berry correspondence

TL;DR

This paper compares the geometric structures of Uhlmann and Berry phases, evaluates the Uhlmann phases of coherent states, and proposes a general correspondence between these phases at zero temperature.

Contribution

It provides a detailed comparison of the Uhlmann and Berry phases using fiber-bundle language and establishes a conditional proof of their correspondence at zero temperature.

Findings

Uhlmann phases carry geometric information and decrease with temperature.

Uhlmann phases approach Berry phases as temperature approaches zero.

Proposes a general zero-temperature correspondence between Uhlmann and Berry phases.

Abstract

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.