In the system of several interacting spins, geometric phases have been
researched intensively.However, the studies are mainly focused on the adiabatic
case (Berry phase), so it is necessary for us to study the non-adiabatic
counterpart (Aharonov and Anandan phase). In this paper, we analyze both the
non-degenerate and degenerate geometric phase of Lipkin-Meskov-Glick type
model, which has many application in Bose-Einstein condensates and entanglement
theory. Furthermore, in order to calculate degenerate geometric phases, the
Floquet theorem and decomposition of operator are generalized. And the general
formula is achieved