# Fidelity Susceptibility in One-dimensional Disordered Lattice Models

## TL;DR

This paper uses fidelity susceptibility to identify quantum critical points and analyze phase transitions in one-dimensional disordered lattice models, revealing different universality classes and potential for experimental observation.

## Contribution

It demonstrates the effectiveness of fidelity susceptibility in locating quantum critical points and determining critical exponents in disordered models, a novel approach in this context.

## Key findings

- Fidelity susceptibility peaks at quantum critical points.
- Critical exponents differ between Anderson and Aubry-André models.
- Potential for experimental observation of fidelity susceptibility in disordered systems.

## Abstract

We investigate quantum phase transitions in one-dimensional quantum disordered lattice models, the Anderson model and the Aubry-Andr\'{e} model, from the fidelity susceptibility approach. First, we find that the fidelity susceptibility and the generalized adiabatic susceptibility are maximum at the quantum critical points of the disordered models, through which one can locate the quantum critical point in disordered lattice models. Second, finite-size scaling analysis of the fidelity susceptibility and of the generalized adiabatic susceptibility show that the correlation length critical exponent and the dynamical critical exponent at the quantum critical point of the one-dimensional Anderson model are respectively 2/3 and 2 and of the Aubry-Andr\'{e} model are respectively 1 and 2.375. Thus the quantum phase transitions in the Anderson model and in the Aubry-Andr\'{e} model are of different universality classes. Because the fidelity susceptibility and the generalized adiabatic susceptibility are directly connected to the dynamical structure factor which are experimentally accessible in the linear response regime, the fidelity susceptibility in quantum disordered systems may be observed experimentally in near future.