Fidelity susceptibility of the anisotropic X Y model: The exact solution

We derive several closed-form expressions for the fidelity susceptibility (FS) of the anisotropic X Y model in the transverse field. The basic idea lies in a partial fraction expansion of the expression so that all the terms are related to a simple fraction or its derivative. The critical points of the model are reiterated by the FS, demonstrating its validity for characterizing the phase transitions. Moreover, the critical exponents ν associated with the correlation length in both critical regions are successfully extracted by the standard finite-size scaling analysis.