Bell inequality and nonlocality in an exactly soluble two-dimensional Ising–Heisenberg spin systems

• Nonlocality in an exactly soluble 2D Ising–Heisenberg spin system is studied.
• Nonlocality identifies the location and the order of the thermal phase transition.
• In anti-ferromagnetic phase, the nonlocality is enhanced by thermal fluctuation.
• In ferromagnetic phase, a novel type of quantum correlation is observed.

In this paper, we use the Bell inequality to study the bipartite correlation in an exactly soluble two-dimensional Ising–Heisenberg spin system. The Bell inequality can detect not only the quantum phase transition, but also the thermal phase transitions, of the system. The property of bipartite correlation in the system is also analyzed. In the quantum anti-ferromagnetic phase, the Bell inequality is violated thus nonlocality is present. It is interesting that the nonlocality is enhanced by thermal fluctuation, and similar results have not been observed in anti-ferromagnetic phases. In the ferromagnetic phase, the quantum correlation turns out to be very novel, which cannot be captured by entanglement or nonlocality.