# Fidelity susceptibility in Gaussian Random Ensembles

## TL;DR

This paper introduces the use of fidelity susceptibility as a dimensionless measure for complex quantum systems, providing analytical distributions for Gaussian ensembles and validating with numerical data.

## Contribution

It analytically derives fidelity susceptibility distributions for Gaussian orthogonal and unitary ensembles, extending its application to complex quantum systems.

## Key findings

- Analytical distributions match numerical data
- Fidelity susceptibility serves as a useful measure for quantum systems
- Applicable to Gaussian orthogonal and unitary classes

## Abstract

The fidelity susceptibility measures sensitivity of eigenstates to a change of an external parameter. It has been fruitfully used to pin down quantum phase transitions when applied to ground states (with extensions to thermal states). Here we propose to use the fidelity susceptibility as a useful dimensionless measure for complex quantum systems. We find analytically the fidelity susceptibility distributions for Gaussian orthogonal and unitary universality classes for arbitrary system size. The results are verified by a comparison with numerical data.