Fidelity susceptibility and geometric phase in critical phenomenon |
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| Authors: | Tian Li-Jun Zhu Chang-Qing Zhang Hong-Biao and Qin Li-Guo |
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| Affiliation: | Department of Physics, Shanghai University, Shanghai 200444, China; Shanghai Key Laboratory for Astrophysics, Shanghai 200234, China; Institute of Theoretical Physics, Northeast Normal University, Changchun 130024, China |
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| Abstract: | Motivated by recent developments in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We obtain the fidelity susceptibilities for SU(2) and SU(1,1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phases in these two systems by calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility is used to explore the two-dimensional XXZ model and the Bose-Einstein condensate (BEC). |
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| Keywords: | fidelity susceptibility geometric phase quantum phase transition |
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