Quantum entanglement and magnon Hall effect on the Lieb lattice model

Entanglement of magnons in the nearest-neighbor Heisenberg model on Lieb lattice (LL) with out-of-plane Dzyaloshinskii-Moriya (DM) antisymmetric spin coupling and external magnetic field is studied. We obtain the behavior of the von Neumann entropy (VN) and concurrence as a function of the DM strength, analyzing the effect of magnon bands on quantum entanglement. Furthermore, the quantum correlations in some fermions models such as the two-dimensional non-Hermitian model (NH) on LL lattice and the tight-binding model (TB) on the LL lattice have been also analyzed. The effect of opening of the gap in the spectrum in these models generates an effect on the entanglement quantifiers as von Neumann entropy, concurrence and negativity.