J. Stein: Unitary flow of the bosonized large-N Lipkin model, J. Phys. G 26 (2000) 377 (Postscript-File)
The flow equations describing the continuous unitary transformation which brings the Hamiltonian closer to diagonality are derived and solved exactly for the Lipkin model in the Holstein-Primakoff boson representation and for a large particle number N. The transformed Hamiltonian is diagonal in order 1/N^3, extending known linear transformations to next-higher orders in the inverse particle number. This approach quite naturally allows to preserve the tridiagonal structure of the original Lipkin Hamiltonian in the course of the transformation. Exact analytical results for the coupling functions and explicit expressions for the ground-state energy and for the energy gap to the first excited state in order 1/N^2 are presented and are compared with the accurate numerical values.