It is well known that all torus are destroyed in the Poincare' section with a certain energy E0 when a classical system is in completely chaotic state. But in its quantum counterpart, the features of the subspace taken up by a coherent state with central energy E0=E0 is not yet clear. In the present paper, taking nuclear Lipkin model as an example, we study the properties of such a subspace taken up by the coherent state of SU(3) group. An effective subspace is obtained by using a new renormalization approach. Our results show that in such an effective subspace the distribution of the nearest level spacings, the elements of effective Hamiltonian matrix, and the one-to-one correspondent map from the subspace of an integrable system to that of nonintegrable one are all consistent with predictions of random matrix theory.
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