Nonlocality of mixtures of the ground and first excited states within J 1 − J 2 Heisenberg model

We investigate both bipartite and multipartite nonlocality in the J 1 − J 2 Heisenberg model. Bipartite nonlocality is measured by the Clauser–Horne–Shimony–Holt inequality, while multipartite nonlocality is explored through Bell-type inequalities. Our findings reveal that neither ground-state nor full thermal-state nonlocality reliably characterizes quantum phase transitions (QPTs). However, we uncover that the mixed-state nonlocality of the ground and first excited states exhibits distinctive characteristics applicable to both bipartite and multipartite scenarios. We also demonstrate how mixed-state quantum correlation behaviors depend on varying temperature regimes. In the bipartite case, we observe a phenomenon known as ‘correlation reversal’ with increasing temperature, a previously unreported occurrence in other models. For the multipartite case, the ability to signify phase transitions is significantly enhanced as the temperature rises. Furthermore, we discover a linear scaling effect that provides valuable insights for extrapolating QPTs in the thermodynamic limit as N → ∞ . Additionally, we identify the critical temperature at which mixed-state nonlocality becomes a reliable indicator of phase transitions.