Characterizing quantum nonlocalities under the Heisenberg XYZ spin model with Dzyaloshinskii–Moriya interaction

Abstract

In quantum information science, the nontrivial applications of the Heisenberg spin model are to realize quantum communication and quantum computing using the quantum nonlocalities between particles in the spin chain. Here, considering Heisenberg XYZ spin model with Dzyaloshinskii–Moriya (DM) interaction, our attentions are directed to ascertain the nonlocal advantage of quantum coherence (NAQC), and also characterize the Bell nonlocality (BN). As revealed from the results, one can use low temperature to realize situations in which the NAQC and BN are invariant. The NAQC and BN cannot be detected if temperature is high. External temperature strongly influences the two quantum nonlocalities in ferromagnetic systems. The strong coupling parameter ℑ x brings on the fact that the two quantum nonlocalities are invariant. It is very difficult to capture the NAQC and BN if ℑ x is weak. Considering ℑ y > 0 , the strong ℑ y is responsible for freezing quantum nonlocalities, and one cannot witness the NAQC when ℑ y is low. Moreover, the freezing of quantum nonlocalities can be achieved via enhancing ℑ z , and the detection of NAQC is difficult if ℑ z is weak. Of particular note, under the influence of DM interactions, NAQC (BN) cannot (can) be frozen both in antiferromagnetic and ferromagnetic systems. The strong D y and D z give rise to the difficulty of capturing the NAQC.