Fidelity spectrum: A tool to probe the property of a quantum phase

Fidelity measures the similarity between two states and is widely adapted by the condensed matter community as a probe of quantum phase transitions in many-body systems. Despite its success in witnessing quantum critical points, information about the fine structure of a quantum phase one can get from this approach is still limited. Here, we proposed a scheme called fidelity spectrum. By studying the fidelity spectrum, one can obtain information about the characteristics of a phase. In particular, we investigated the spectra in the one-dimensional transverse-field Ising model and the two-dimensional Kitaev model on a honeycomb lattice. It was found that the spectra have qualitative differences in the critical and non-critical regions of the two models. From the distributions of them, the dominating k modes in a particular phase could also be captured.