Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states

• URL: http://arxiv.org/abs/2403.06944v2
• Date: Wed, 29 May 2024 13:43:24 GMT
• Title: Sj$\ddot{\text{o}}$qvist quantum geometric tensor of finite-temperature mixed states
• Authors: Zheng Zhou, Xu-Yang Hou, Xin Wang, Jia-Chen Tang, Hao Guo, Chih-Chun Chien,
• Abstract summary: The quantum geometric tensor (QGT) reveals local geometric properties and associated topological information of quantum states. We develop a generalization of the QGT to mixed quantum states at finite temperatures based on the Sj$ddottexto$qvist distance. A Pythagorean-like relation connects the distances and gauge transformations, which clarifies the role of the parallel-transport condition.
• Score: 7.482978776412444
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum geometric tensor (QGT) reveals local geometric properties and associated topological information of quantum states. Here a generalization of the QGT to mixed quantum states at finite temperatures based on the Sj$\ddot{\text{o}}$qvist distance is developed. The resulting Sj$\ddot{\text{o}}$qvist QGT is invariant under gauge transformations of individual spectrum levels of the density matrix. A Pythagorean-like relation connects the distances and gauge transformations, which clarifies the role of the parallel-transport condition. The real part of the QGT naturally decomposes into a sum of the Fisher-Rao metric and Fubini-Study metric, allowing a distinction between different contributions to the quantum distance. The imaginary part of the QGT is proportional to a weighted summation of the Berry curvatures, which leads to a geometric phase for mixed states under certain conditions. We present three examples of different dimensions to illustrate the temperature dependence of the QGT and a discussion on possible implications.

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