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Lipkin

The Lipkin model

1. You can read about the Lipkin model in the original paper by Harry Lipkin and collaborators(Attach:lipkin.pdf)
   • The Lipkin model is defined by Eq. (2.1) and setting W=0
   • Find the eigenvalues for N=2 particles by diagonalizing the Hamiltonian matrix formed by Eq. (2.1)
   • Derive the 8 x 8 Hamiltonian matrix of Eq. (2.1) for N=3 particles
   • Using Eq. (2.2), derive Eq. (2.3)
   • Using the quasi-spin formulation, Eq. (2.4), find the analytical expression for the energy eigenvalues in the N=3 case
   • H. Lipkin lists the analytical expression for the energy in systems with N=2,3,4,6,8