Interplay of spin Nernst effect and entanglement negativity in Lieb lattice ferromagnets: An exact diagonalization study

We analyze the influence of the spin Nernst effect on entanglement in trimerized Lieb lattice ferromagnets, with Dzyaloshinskii-Moriya interaction (DMI) out-of-plane and single ion anisotropy. We get the behavior of the entanglement negativity as a function of the temperature for different strength of DMI with aim to verify the influence of topological phase transition on entanglement. Moreover, we get the effect of the variation of the spin Nernst coefficient with DMI on entanglement negativity. We get that the effect of opening of the gap of topological magnons generates a small variation in the behavior of the entanglement negativity. The analyze of the influence of the spin Nernst effect on entanglement in trimerized Lieb lattice ferromagnets, especially in the context of DMI interaction and single-ion anisotropy, is a complex and intriguing task. Thus, we focus on understanding how these interactions and topological transitions affect entanglement negativity and the spin Nernst coefficient.