Thermal quantum coherence of two-qutrit Heisenberg XXZ model with Herring-Flicker coupling and Dzyaloshinskii-Moriya interaction under magnetic field

In this study, we use the concept of \(l_1\)-norm coherence to characterize the entanglement of a two--qutrit Heisenberg XXZ model for subject to a uniform magnetic field and z--axis Dzyaloshinskii--Moriya interaction with Herring-Flicker coupling. We show the temperature, magnetic field, DM interaction, and distance of Herring-Flicker coupling all can control the entanglement. However, the state system becomes less entangled at high temperatures or strong magnetic fields and vice versa. Our findings also suggest that entanglement rises when the z--axis DM interaction increases. Moreover, by setting the strengths coupling of the spin, we quickly recover the isotropic XY and XXX Heisenberg models. Finally, Herring-Flicker coupling affects the degree of entanglement. In fact, when Herring-Flicker coupling and temperature are at small values, the degree of entanglement is at its highest. Still, when Herring-Flicker coupling is at substantial values, the degree of entanglement tends to stabilize.