Multipartite nonlocality spectrum and quantum criticality in one-dimensional quantum chains

Multipartite nonlocality is a measure of multipartite quantum correlations, and has been used to characterize quantum criticality in various low-dimensional quantum models. In this work, we propose the nonlocality spectrum ${|{\ensuremath{\lambda}}_{i}|}$ of the nonlocality transfer matrix as a tool to characterize multipartite nonlocality and quantum criticality in infinite-size translation-invariant quantum systems. The approach is used to analyze four typical quantum spin chain models, i.e., the transverse-field Ising model, an XXZ model, a three-body coupling cluster model and an XYZ model. In various types of quantum phase transitions in these models, it is found that at the critical points, the leading eigenvalue $|{\ensuremath{\lambda}}_{1}|$ presents identifiable signals, and the spectrum gap $\mathrm{\ensuremath{\Delta}}|\ensuremath{\lambda}|=|{\ensuremath{\lambda}}_{1}|\ensuremath{-}|{\ensuremath{\lambda}}_{2}|$ closes. Moreover, the nonlocality spectrum provides a unified mathematical framework to reveal the underlying mechanisms for various previously reported behaviors of multipartite nonlocality. Our results demonstrate the power of the nonlocality spectrum as a valuable tool for the comprehensive characterization of multipartite nonlocality and quantum criticality in one-dimensional quantum systems.