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Summary
The study investigates the topological phase transition of Kitaev spin liquid in an external magnetic field by calculating the Berry curvature and the Fubini-Study metric. The results show that the xy-component of the Berry curvature has the same behavior around the critical lines as the phase diagram, and the Fubini-Study metric is highly correlated with the phase diagram.
Highlights
- The Kitaev spin liquid model is studied in an external magnetic field.
- The Berry curvature and Fubini-Study metric are calculated.
- The xy-component of the Berry curvature jumps around the critical lines.
- The Fubini-Study metric is highly correlated with the phase diagram.
- The phase transition is characterized by the derivative of the total effective spin magnetic susceptibility.
- The Uhlmann curvature is calculated for the finite-temperature system.
- The Bures metric is generalized from pure states to mixed states.
Key Insights
- The study reveals that the topological phase transition of Kitaev spin liquid is characterized by the jumping of the xy-component of the Berry curvature around the critical lines, which is related to the derivative of the total effective spin magnetic susceptibility.
- The Fubini-Study metric is found to be highly correlated with the phase diagram, indicating that it can be used to characterize the phase transition.
- The Uhlmann curvature is calculated for the finite-temperature system, and it is found to have a peak at the critical point of the phase transition.
- The Bures metric is generalized from pure states to mixed states, and it is found to have an additional term called the Fisher-Rao metric caused by the mixed state.
- The study demonstrates that the geometric tensor can be used to characterize the phase transition of Kitaev spin liquid.
- The results show that the phase transition is robust against local perturbation.
- The study provides a new perspective on the phase transition of Kitaev spin liquid by using the geometric tensor and the Uhlmann curvature.
Mindmap
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Citation
Lu, M.-M., & Wang, Z.-C. (2024). Phase transition of Kitaev spin liquid described by quantum geometric tensor (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.20889