Topological Uhlmann phase transitions for a spin-j particle in a magnetic field

Abstract

The generalization of the geometric phase to the realm of mixed states is known as Uhlmann phase. Recently, applications of this concept to the field of topological insulators have been made and an experimental observation of a characteristic critical temperature at which the topological Uhlmann phase disappears has also been reported. Surprisingly, to our knowledge, the Uhlmann phase of such a paradigmatic system as the spin-$j$ particle in presence of a slowly rotating magnetic field has not been reported to date. Here we study the case of such a system in a thermal ensemble. We find that the Uhlmann phase is given by the argument of a complex valued second kind Chebyshev polynomial of order $2j$. Correspondingly, the Uhlmann phase displays $2j$ singularities, occurying at the roots of such polynomials which define critical temperatures at which the system undergoes topological order transitions. Appealing to the argument principle of complex analysis each topological order is characterized by a winding number, which happen to be $2j$ for the ground state and decrease by unity each time increasing temperature passes through a critical value. We hope this study encourages experimental verification of this phenomenon of thermal control of topological properties, as has already been done for the spin-$1/2$ particle.

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Cited by in corpus (14)

• Finite-temperature topological phase transitions of spin-$j$ systems in Uhlmann processes: General formalism and experimental protocols
• Geometric phases of mixed quantum states: A comparative study of interferometric and Uhlmann phases
• Uhlmann phase of coherent states and the Uhlmann-Berry correspondence
• Uhlmann quench and geometric dynamic quantum phase transition of mixed states
• Uhlmann holonomy against Lindblad dynamics of topological systems at finite temperatures
• Proxy ensemble geometric phase and proxy index of time-reversal invariant topological insulators at finite temperatures
• Geometric phases of Topological Systems under Quench Process
• Thermal Uhlmann phase in a locally driven two-spin system
• The Uhlmann Phase Winding in Bose-Einstein Condensates at Finite Temperature
• Mixed-state geometric phases of coherent and squeezed spin states
• Uhlmann phase in composite systems with entanglement
• Uhlmann and scalar Wilczek-Zee phases of degenerate quantum systems
• Comparison of finite-temperature topological indicators based on Uhlmann connection
• Interferometric Geometric Phases of $\mathcal{P}\mathcal{T}$-symmetric Quantum Mechanics