Effect of one-ion L-S coupling on magnetic properties of a correlated spin-orbit system

By introducing a basis for a novel realization of the SU(4) Lie algebra, we exactly solve a spin-orbital chain with one-ion $L$-$S$ coupling (OILSC) via the Bethe ansatz (BA) approach. In the context of different Land\'e $g$ factors of the spin and orbital sectors, the OILSC results in rich and novel quantum phase transitions. Some accurate analytical expressions for the critical fields are obtained. Both spin ordering and orbital ordering are found in a gapped singlet phase. The system exhibits many interesting phenomena such as nonvanishing magnetization of the singlet phase, multi-entrance of the singlet in the ground state when the field varies, unsymmetric magnetization in two-component phase and magnetization crossover for different OILSC.