Phase transitions in the two-dimensional Anisotropic Biquadratic Heisenberg Model

In this paper we study the influence of the single-ion anisotropy in the two-dimensional biquadratic Heisenberg model (ABHM) on the square lattice at zero and finite low temperatures. It is common to represent the bilinear and biquadratic terms by J1=Jcosθ and J2=Jsinθ, respectively, and the many phases present in the model as a function of θ are well documented. However we have adopted a constant value for the bilinear constant (J1=1) and small values of the biquadratic term (|J2|Dc, the excited states are gapped and there is no spin long-range order (LRO) even at zero temperature. Using Schwinger bosonic representation and Self-Consistent Harmonic Approximation (SCHA), we have studied the quantum and thermal phase transitions as a function of the bilinear and biquadratic constants. - Highlights: • We study the anisotropic biquadric bilinear Heisenberg model on a square lattice. • We show the quantum phase transition associated with the anisotropic constant. • We obtain a thermal phase transition similar to the BKT transition