Detection of avoided crossings by fidelity

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

Research highlights
► We propose fidelity as an efficient detector of avoided crossings in energy spectra.
► Fidelity allows local as well as global statistical characterization of spectra.
► Our fidelity measure can be used for analyzing complex quantum systems.
► Results are verified for a random matrix model and a Bose–Hubbard system.