Fidelity susceptibility in the two-dimensional transverse field Ising and XXZ models

TL;DR

This paper numerically investigates fidelity susceptibility in 2D transverse field Ising and XXZ models, confirming its divergence at critical points and its effectiveness in detecting quantum phase transitions.

Contribution

It demonstrates that fidelity susceptibility reliably signals quantum phase transitions in 2D models and compares its scaling behavior to energy derivatives.

Findings

Fidelity susceptibility diverges at critical points in both models.

It confirms fidelity susceptibility as a sensitive indicator of second order quantum phase transitions.

The scaling behavior of fidelity susceptibility's extremum supports its theoretical advantage.

Abstract

We study the fidelity susceptibility in the two-dimensional(2D) transverse field Ising model and the 2D XXZ model numerically. It is found that in both models, the fidelity susceptibility as a function of the driving parameter diverges at the critical points. The validity of the fidelity susceptibility to signal for the quantum phase transition is thus verified in these two models. We also compare the scaling behavior of the extremum of the fidelity susceptibility to that of the second derivative of the ground state energy. From those results, the theoretical argument that fidelity susceptibility is a more sensitive seeker for a second order quantum phase transition is also testified in the two models.