Abstract
We mainly explore the fidelity susceptibility based on the Lie algebraic method. On physical grounds, the exact expressions of fidelity susceptibilities can be respectively obtained in SU(2) and SU(1,1) algebraic structure models, which are applied to one-body system and many-body systems, such as the single spin model, the single-mode squeeze harmonic oscillator model and the BCS model. In terms of the double-time Green-function method, our general conclusions are illustrated with two models which exhibit the fidelity susceptibilities at the finite temperature and T = 0.
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