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 J(1) = J cos phi and J(2) = J sin phi, respectively, and the many phases present in the model as a function of phi are well documented. However we have adopted a constant value for the bilinear constant (J(1) = 1) and small values of the biquadratic term (vertical bar J(2)vertical bar < J(1)). Specially, we have analyzed the quantum phase transition due to the single-ion anisotropic constant D. For values below a critical anisotropic constant D-c the energy spectrum is gapless and at low finite temperatures the order parameter correlation has an algebraic decay (quasi-long-range order). Moreover, in D < D-c phase there is a transition temperature where the quasi-long-range order (algebraic decay) is lost and the decay becomes exponential, similar to the Berezinski-Kosterlitz-Thouless (BKT) transition. For D > D-c, 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. (C) 2014 Elsevier B.V. All rights reserved.