Fidelity susceptibility of the anisotropic $XY$ model: The exact solution

TL;DR

This paper provides exact formulas for the fidelity susceptibility of the anisotropic XY model, demonstrating its effectiveness in identifying phase transitions and extracting critical exponents through finite-size scaling.

Contribution

It presents the first exact solutions for the fidelity susceptibility of the anisotropic XY model in a transverse field, enhancing understanding of quantum phase transitions.

Findings

Fidelity susceptibility accurately signals phase transitions.

Derived closed-form expressions for FS using partial fraction expansion.

Extracted critical exponents consistent with theoretical predictions.

Abstract

We derive several closed-form expressions for the fidelity susceptibility~(FS) of the anisotropic $XY$ 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 $\nu$ associated with the correlation length in both critical regions are successfully extracted by the standard finite-size scaling analysis.