Quantum entanglement in the bilinear-biquadratic model for iron-based superconductors

Recently there has been a renewed interest in biquadratic exchange interactions in recently discovered two-dimensional magnets.  In a general way, biquadratic interactions are present in spin-1 magnets being known as to favor nematic ordering.[1-10] In this work we study quantum correlation in the spin-1 two-dimensional Heisenberg model on square lattice with biquadratic interactions and the next-nearest neighboring interaction or bilinear-biquadratic (BBQ) model is investigated. The calculations were performed for the model in the quadrupolar phases using SU(3) flavor-wave theory. We calculate the von Neumann entropy as a function of the biquadratic couplings, J_bq1, J_bq2 and next-nearest neighboring exchange interaction of the lattice with aim to very the effect of different phase transitions as the phase transition Néel-quadrupolar on quantum entanglement.