Nonlocality in the alternating Heisenberg–Ising spin chain: effects of coupling, magnetic field, and temperature

Abstract

We explore bipartite and multipartite nonlocality in the alternating Heisenberg–Ising spin chain model, emphasizing the contrasting and complementary roles of the relative coupling strength \(\lambda \) (the ratio of the Ising interaction to the Heisenberg interaction), the external magnetic field h, and the temperature T. Bipartite nonlocality is evaluated using the CHSH inequality, and multipartite nonlocality is assessed through Bell-type inequalities derived from g-grouping model theory. Our results show that \(\lambda \), h, and T significantly affect nonlocality in distinct ways. Increasing \(\lambda \) suppresses bipartite nonlocality but enhances multipartite nonlocality, highlighting the interaction-specific roles in the system: The Heisenberg interaction primarily governs bipartite nonlocal correlations, whereas the Ising interaction drives multipartite nonlocal correlations. In contrast, both h and T universally suppress bipartite and multipartite nonlocal correlations, irrespective of the interaction type. We also reveal scaling behaviors of nonlocality near the quantum critical points, denoted as \(\lambda _{c}\), where both bipartite and multipartite nonlocality exhibit clear signatures in their first derivatives. Critical scaling is described by \(\lambda _{c}(N) = \lambda _{c}(\infty )-aN^{-b}\), allowing precise determination of the critical value \(\lambda _{c}(\infty ) = 2\) in the thermodynamic limit.