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We study the effect of symmetry breaking perturbations in the one-dimensionalSU(4) spin-orbital model. We allow the exchange in spin ($J_1$) and orbital($J_2$) channel to be different and thus reduce the symmetry to SU(2) $\otimes$SU(2). A magnetic field $h$ along the $S^z$ direction is also applied. Usingthe formalism developped by Azaria et al we extend their analysis of theisotropic $J_1=J_2$, h=0 case and obtain the low-energy effective theory nearthe SU(4) point in the asymmetric case. An accurate analysis of therenormalization group flow is presented with a particular emphasis on theeffect of the anisotropy. In zero magnetic field, we retrieve the samequalitative low-energy physics than in the isotropic case. In particular, themassless behavior found on the line $J_1=J_2>K/4$ extends in a largeanisotropic region. We discover though that the anisotropy plays its trick inallowing non trivial scaling behaviors of the physical quantities. When amagnetic field is present the effect of the anisotropy is striking. In additionto the usual commensurate-incommensurate phase transition that occurs in thespin sector of the theory, we find that the field may induce a secondtransition of the KT type in the remaining degrees of freedom to which it doesnot couple directly. In this sector, we find that the effective theory is thatof an SO(4) Gross-Neveu model with an h-dependent coupling that may change itssign as h varies.Comment: 14 pages, 5 Figs, added referenc

physical review. b, condensed matter

Effect of symmetry-breaking perturbations in the one-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">SU</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mn>4</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:math>spin-orbital model

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