Phase transitions in the two-dimensional Anisotropic Biquadratic Heisenberg Model

Abstract

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|<J1). Specially, we have analyzed the quantum phase transition due to the single-ion anisotropic constant D. For values below a critical anisotropic constant Dc 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<Dc 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>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.