The temperature dependent geometric phase

Zheng-Chuan Wang

Zheng-Chuan Wang

There exists a geometric phase for a quantum state during the adiabatic evolution of the system. If the adiabatic procedure happens between the system and the environment interacting with it similar to Born-Oppenheimer (BO) approximation, we can introduce a temperature into the environment, which can be regarded as in an equilibrium state. Then a temperature-dependent geometric phase can be obtained for the system, which originates from the Abelian gauge potential induced by the BO approximation. This gauge potential contributes to the effective potential of the system, which is temperature dependent, too. Finally, we demonstrate them using an example of H_2^+ ion system.

Harald Grosse, W. L. Kennedy

Xu-Yang Hou, Xin Wang, Hao Guo

Geometric phases play a fundamental role in understanding the geometric structure of quantum states, yet extending the Uhlmann phase to non-Hermitian systems poses significant challenges due to parameter-dependent inner product structures. In this work, we develop a comprehensive theory of the Uhlmann phase for quasi-Hermitian systems, where the physical Hilbert space metric varies with external parameters. By constructing a generalized purification that respects the quasi-Hermitian inner product, we derive the corresponding parallel transport condition and Uhlmann connection. Our analysis reveals that the parameter-dependent metric modifies the Uhlmann connection and leads to a finite-temperature distribution of Uhlmann-phase regions that differs from the standard Hermitian case. Applying this formalism to solvable two-level models, we uncover tunable finite-temperature Uhlmann-phase diagrams, where the parameter-dependent metric shifts and deforms the zeros of the Uhlmann amplitude, thereby reshaping the temperature intervals in which nontrivial Uhlmann phases occur. Furthermore, by extending established interferometric protocols originally developed for Hermitian systems, the geometric amplitude can be recast as a measurable Loschmidt amplitude between purified states, providing a practical and experimentally accessible pathway to investigate quasi-Hermitian mixed-state geometric phases and their finite-temperature transitions. This work establishes a unified framework for understanding mixed-state geometric phases in quasi-Hermitian quantum systems and, through its natural relation to the mixed-state quantum geometric tensor, opens new avenues for exploring local geometry in quasi-Hermitian thermal states.

Aiping Zhang, Wen-Chao Qiang, Ya-Wen Ling +2 more

We study the geometric phase of a qutrit-qubit mixed-spin system in an external homogeneous magnetic field. Both the spin-spin interaction strength J and the external magnetic field B can affect the geometric phase of the system. In addition, we consider the negativity of the composite system. The relationship between the negativity and the geometric phase is obtained. Finally, we calculate the geometric phase for a thermal mixed state and show how the geometric phase depends on the rescaled coupling parameter and temperature. In the limit T → 0, we can recover the result of the ground state. This analysis has some implications in realistic implementations of geometric quantum computation.

Wolfhard Janke E, Adriaan M. J. Schakel