Adiabatic approximation in the second quantized formulation

Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and unambiguous criterion of the adiabatic approximation. This is illustrated for the model of Marzlin and Sanders [Phys. Rev. Lett. 93, 160408 (2004)] and a model related to the geometric phase which can be exactly diagonalized in the present sense