Symmetry-adapted BCS-type trial wave functions for mesoscopic rings

In mesoscopic systems, the symmetry of the wave function cannot be broken and must be considered. We construct symmetry-adapted trial wave functions of the Bardeen-Cooper-Schrieffer-type for mesoscopic rings described by an extended-Hubbard model at half-filling. The comparison with exact numerical (Lanczos) diagonalization in small rings indicates that this variational approach is reasonably accurate. Within this approach, we demonstrate a crossover from a weak-correlation regime to a strong correlation one. Particularly interesting is the behavior of the lowest-excitation energy, which switches from a highest-occupied-molecular-orbital–lowest-unoccupied-molecular-orbital gap to a splitting energy related to a collective tunneling of electrons.