Uhlmann and scalar Wilczek-Zee phases of degenerate quantum systems

Fuente: arXiv
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Main Authors: Wang, Xin, Guo, Hao, Chien, Chih-Chun
Format: Preprint
Published: 2025
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author Wang, Xin
Guo, Hao
Chien, Chih-Chun
author_facet Wang, Xin
Guo, Hao
Chien, Chih-Chun
contents The Wilczek-Zee (WZ) holonomy arises in degenerate states while the Uhlmann holonomy characterizes finite-temperature topology. We investigate possible relationships between the Uhlmann phase and the scalar WZ phase, which reflects the Uhlmann and WZ holonomy respectively, in an exemplary four-level model with two doubly degenerate subspaces. Through exact solutions, we contrast the behavior of the Uhlmann and WZ connections and their associated phases. In the zero-temperature limit, the Uhlmann phase may or may not agree with the scalar WZ phase of the degenerate ground states due to obstructions from the Hamiltonian manifested as Dirac points. This is in stark contrast to non-degenerate systems where the correspondence between the Uhlmann and Berry phases in general holds. Our analyses further show that for the example studied here, the Uhlmann phase catches the singular behavior at the Dirac points while the WZ connection and scalar WZ phase vanish along a zero-field axis. We also briefly discuss possible experimental implications.
format Preprint
id arxiv_https___arxiv_org_abs_2505_15609
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Uhlmann and scalar Wilczek-Zee phases of degenerate quantum systems
Wang, Xin
Guo, Hao
Chien, Chih-Chun
Quantum Physics
Mesoscale and Nanoscale Physics
The Wilczek-Zee (WZ) holonomy arises in degenerate states while the Uhlmann holonomy characterizes finite-temperature topology. We investigate possible relationships between the Uhlmann phase and the scalar WZ phase, which reflects the Uhlmann and WZ holonomy respectively, in an exemplary four-level model with two doubly degenerate subspaces. Through exact solutions, we contrast the behavior of the Uhlmann and WZ connections and their associated phases. In the zero-temperature limit, the Uhlmann phase may or may not agree with the scalar WZ phase of the degenerate ground states due to obstructions from the Hamiltonian manifested as Dirac points. This is in stark contrast to non-degenerate systems where the correspondence between the Uhlmann and Berry phases in general holds. Our analyses further show that for the example studied here, the Uhlmann phase catches the singular behavior at the Dirac points while the WZ connection and scalar WZ phase vanish along a zero-field axis. We also briefly discuss possible experimental implications.
title Uhlmann and scalar Wilczek-Zee phases of degenerate quantum systems
topic Quantum Physics
Mesoscale and Nanoscale Physics
url https://arxiv.org/abs/2505.15609