Detection of avoided crossings by fidelity

TL;DR

This paper introduces the use of fidelity, the overlap of eigenstates from slightly different Hamiltonians, as an efficient method to detect avoided crossings in quantum energy spectra, applicable to complex systems.

Contribution

It proposes a novel application of fidelity for identifying avoided crossings, demonstrated on model and complex quantum systems.

Findings

Fidelity effectively detects avoided crossings in various quantum models.

Application to random matrix and Bose-Hubbard systems shows broad utility.

Fidelity provides a practical tool for spectral analysis in quantum physics.

Abstract

The fidelity, defined as overlap of eigenstates of two slightly different Hamiltonians, is proposed as an efficient detector of avoided c rossings in the energy spectrum. This new application of fidelity is motivated for model systems, and its value for analyzing complex qua ntum spectra is underlined by applying it to a random matrix model and a tilted Bose-Hubbard system.