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In this study, we use the concept of $l_1$-norm coherence to characterize theentanglement of a two--qutrit Heisenberg XXZ model for subject to a uniformmagnetic field and z--axis Dzyaloshinskii--Moriya interaction withHerring-Flicker coupling. We show the temperature, magnetic field, DMinteraction, and distance of Herring-Flicker coupling all can control theentanglement. However, the state system becomes less entangled at hightemperatures or strong magnetic fields and vice versa. Our findings alsosuggest that entanglement rises when the z--axis DM interaction increases.Moreover, by setting the strengths coupling of the spin, we quickly recover theisotropic XY and XXX Heisenberg models. Finally, Herring-Flicker couplingaffects the degree of entanglement. In fact, when Herring-Flicker coupling andtemperature are at small values, the degree of entanglement is at its highest.Still, when Herring-Flicker coupling is at substantial values, the degree ofentanglement tends to stabilize.

physica scripta

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