Antônio R. Moura, Antônio S. T. Pires, Afrânio R. Pereira
In this paper we study the two-dimensional anisotropic biquadratic Heisenberg model (ABHM) on the square lattice at zero and finite low temperatures. The model presents many phases due to both biquadratic and anisotropic terms. Its features in one-dimensional systems are well-documented. For the two-dimensional case, however, there are regions which are not so clear and, therefore, more investigations are necessary. In special, we have analyzed the quantum phase transition due to the single-ion anisotropic constant $D$. For values below a critical anisotropic constant $D_c$ (i.e., for $D < D_c$), the energy spectrum is gapless and, at low finite temperatures, the order parameter correlation has an algebraic decay (quasi long-range order). There are a transition temperature where the quasi long-range order is lost and the decay becomes an exponential, similar to the Berezinski-Kosterlitz-Thouless (BKT) transition. For $D > D_c$, the excited states are gapped and there is no 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.
View original:
http://arxiv.org/abs/1305.6305
No comments:
Post a Comment