Finite-temperature topological phase transitions of spin-$j$ systems in Uhlmann processes: General formalism and experimental protocols

Abstract

The Uhlmann process is built on the density matrix of a mixed quantum state and offers a way to characterize topological properties at finite temperatures. We analyze an ideal spin-j quantum paramagnet in a magnetic field undergoing an Uhlmann process and derive general formulae of the Uhlmann phase and Loschmidt amplitude for arbitrary j as the system traverses a great circle in the parameter space. A quantized jump of the Uhlmann phase signifies a topological quantum phase transition (TQPT) of the underlying process, which is accompanied by a zero of the Loschmidt amplitude. The exact results of j=1/2 and j=1 systems show topological regimes that only survive at finite temperatures but not at zero temperature, and the number of TQPTs is associated with the winding number in the parameter space. Our results pave the way for future studies on finite-temperature topological properties, and possible experimental protocols and implications for atomic simulators and digital simulations are discussed.

arXiv comment16 pages, 5 figures

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• Uhlmann holonomy against Lindblad dynamics of topological systems at finite temperatures
• Aperiodic dynamical quantum phase transitions in multi-band Bloch Hamiltonian and its origin
• Generalizations of Berry phase and differentiation of purified state and thermal vacuum of mixed states
• Proxy ensemble geometric phase and proxy index of time-reversal invariant topological insulators at finite temperatures
• Geometric phases of Topological Systems under Quench Process
• Geometry effect of the dynamical quantum phase transitions at finite temperatures
• 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 and scalar Wilczek-Zee phases of degenerate quantum systems
• Interferometric Geometric Phases of $\mathcal{P}\mathcal{T}$-symmetric Quantum Mechanics
• Comparison of finite-temperature topological indicators based on Uhlmann connection