Abstract
By building a multi-fermion realization of the quantum algebra SU q (2), we generalized the Lipkin-Meshkov-Glick (LMG) model to test the validity of many-body approximation methods. Our general LMG model incorporates the quantum group symmetry of SU q (2) and the many-body force besides the two-body one in many-fermions systems, which give a probe of the dynamic process that the quantum group symmetry should describe. The exact solvability is still guaranteed by the finite dimensional representation of SU q (2). The deformation parameter q is introduced in the generalized model to characterize the difference between this model and the original one. Especially, it leads to the crossing of different energy levels.
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