Influence of the site dilution on quantum phase transition of the biquadratic Heisenberg model at low dimension

We use the SU(3) Schwinger's boson formalism to study the quantum phase transition of the S=1 biquadratic Heisenberg model in one and two dimensions, (1D) and (2D), with non-magnetic impurities on the lattice. In the 2D case, we consider the square lattice. We have verified the influence of the site dilution in the dependence of the gap with the force of coupling of the biquadratic term, β, on the Bose-Einstein condensation. Our results show that the inclination of the curve of decreasing of the gap with the −β parameter changes. However, the value of −β where the gap cancel does not change. We also obtain that the exciton energy cancels in a concentration of non-magnetic impurities x→0.5 indicating therefore, an absence of quasi-particles (excitons) to form a spin current in this concentration of impurities.