Effect of symmetry-breaking perturbations in the one-dimensional SU(4) spin-orbital model

We study the effect of symmetry-breaking perturbations in the one-dimension al SU(4) spin-orbital model. We allow the exchange in spin (J(1)) and orbit al (J(2)) channel to be different and thus reduce the symmetry to SU(2) x S U(2). A magnetic field h along the S-z direction is also applied. Using the formalism developed by Azaria er al. [Phys. Rev. Lett. 83, 624 (1999)] we extend their analysis of the isotropic J(1)=J(2), h=0 case and obtain the l ow-energy effective theory near the SU(4) point in the generic case J(1)not equal J(2), h not equal 0. In zero magnetic field, we retrieve the same qu alitative low-energy;physics as in the isotropic case. In particular, the i sotropic massless behavior found on the line J(1)=J(2)<K/4 extends in a lar ge anisotropic region. We discover, however, that the anisotropy plays its trick in allowing nontrivial scaling behaviors of the physical quantities. For example, the mass gap M has two different scaling behaviors depending o n the anisotropy. In addition, we show that in some regions, the anisotropy is responsible for anomalous finite-size effects and may change qualitativ ely the shape of the computed critical line in a finite system. When a magn etic field is present the effect of the anisotropy is striking. In addition to the usual commensurate-incommensurate phase transition that occurs in t he spin sector of the theory, we find that the field may induce a second tr ansition of the KT type in the remaining degrees of freedom to which it doe s nor couple directly. In this sector, we find that the effective theory is that of an SO(4) Gross-Neveu model with an h-dependent coupling that may c hange its sign as h varies.