Fidelity susceptibility in Gaussian random ensembles

Area of Science:

• Quantum mechanics
• Statistical physics

Background:

• Fidelity susceptibility quantifies the sensitivity of quantum system eigenstates to external parameter changes.
• It is a powerful tool for identifying quantum phase transitions in ground and thermal states.

Purpose of the Study:

• To propose and validate fidelity susceptibility as a dimensionless measure for complex quantum systems.
• To analytically derive fidelity susceptibility distributions for specific universality classes.

Main Methods:

• Analytical derivation of fidelity susceptibility distributions.
• Investigation of Gaussian orthogonal and unitary universality classes.
• Comparison with numerical data for verification.

Main Results:

• Analytical expressions for fidelity susceptibility distributions were obtained for arbitrary system sizes.
• The derived distributions are applicable to Gaussian orthogonal and unitary universality classes.
• Numerical data confirmed the accuracy of the analytical results.

Conclusions:

• Fidelity susceptibility is a versatile and effective dimensionless measure for analyzing complex quantum systems.
• The analytical framework provides a robust method for characterizing quantum phase transitions.
• The findings offer valuable insights into the behavior of quantum systems across different universality classes.