The two-level pairing model in the Schwinger representation

Abstract

The two-level pairing model was investigated in the framework of the Schwinger representation. It has been shown that zero-point fluctuations, which are important in the crossover region, are well described by certain coherent states which conserve the constants of motion. These so-called conserving approximations provide excellent descriptions of the ground-state energy and of the first excitation energy over the whole range of coupling constant values. The description of the ground-state energy provided by the Glauber coherent state is also reasonable, but not so good. Although the Glauber coherent state fails to provide the description of the excitation energy around the critical point, its performance in the strong coupling limit is very good both for the description of the ground-state energy and of the first excitation energy. The present results also show that already at the mean-field level, the bosonic description in the independent particle approximation incorporates important correlation corrections to the conventional mean-field description based on the fermionic realization of the su(2) algebra (BCS theory).