Effects of a magnetic field on the one-dimensional spin-orbital model

We study the effects of a uniform magnetic field on the one-dimensional spin-orbital model in terms of effective field theories. Two regions are examined: one around the SU(4) point (J=K/4) and the other with K much less than J [see Eq. (1)]. We found that when J less than or equal to K/4, the spin and orbital correlation functions exhibit power-law decay with nonuniversal exponents. In the region with J>K/4, the excitation spectrum has a gap but the structure of it changes at different range of the ratio J/K. Furthermore, near the SU(4) point, the magnetic field exerts a great influence on the spectrum of the S-Z=0 sector. When the magnetic field is beyond Some critical value, a quantum phase transition occurs. The different structure of the excitation spectrum results in distinct critical behavior of correlation functions around the SU(4) point and the region with K much less than J. Especially, the exponents in the latter case are universal.