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 $J_1=J\cos \theta$ and $J_2=J\sin \theta$, respectively, and it is well documented the many phases present in the model as function of $\theta$. However we have adopted a constant value for the bilinear constant ($J_1=1$) and small values of the biquadratic term ($|J_2|<J_1$). In special, 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 are a transition temperature where the quasi long-range order (algebric 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.

11 pages, 12 figures

References in corpus (3)

• Spin nematic correlations in bilinear-biquadratic S=1 spin chains
• Exotic S=1 spin liquid state with fermionic excitations on triangular lattice
• Non-linear dynamics and two-dimensional solitons for spin $S=1$ ferromagnets with biquadratic exchange

Cited by in corpus (3)

• Theoretical analysis of FMR-driven spin pumping current and its properties via Self-Consistent Harmonic Approximation
• Phase transitions in the two-dimensional single-ion anisotropic ferromagnetic with long-range interactions
• Effectiveness of the Self-Consistent Harmonic Approximation in ferromagnets with dipolar interactions