Multipartite nonlocality spectrum and topological quantum phase transitions in a one-dimensional extended quantum Ising model

The extended quantum Ising model serves as a paradigmatic model for studying topological quantum phase transitions (TQPTs), which entail fundamental changes in the system's global topological order. In this work, we employ nonlocality spectrum $\left\{\right|{\lambda }_i\left|\right\}$ as the central tool to probe multipartite nonlocal correlations and quantum criticality in this model. Our analysis reveals that the leading one in the spectrum satisfies $\left|{\lambda }_1\right|>1$ in most parameter regimes, confirming pervasive multipartite nonlocal correlations in the ground states. Furthermore, the spectral gap $\Delta \left|\lambda \right|$ universally vanishes at all TQPT points in the model, establishing it as a robust and derivative-free marker for TQPTs. These results highlight the utility of nonlocality spectrum in characterizing both multipartite nonlocal correlations and TQPTs in one-dimensional (1D) quantum systems.