  In purely repulsive, $C_{4v}$-symmetric Hubbard clusters a correlation effect
produces an effective two-body attraction and pairing; the key ingredient is
the availability of W=0 pairs, that is, two-body solutions of appropriate
symmetry. We study the tunneling of bound pairs in rings of 5-site units
connected by weak intercell links; each unit has the topology of a CuO$_{4}$
cluster and a repulsive interaction is included on every site. Further, we test
the superconducting nature of the response of this model to a threading
magnetic field. We present a detailed numerical study of the two-unit ring
filled with 6 particles and the three-unit ring with 8 particles; in both cases
a lower filling yields normal behavior. In previous studies on 1d Hubbard
chains, level crossings were reported (half-integer or fractional Aharonov-Bohm
effect) which however cannot be due to superconducting pairs. In contrast, the
nontrivial basis of clusters carrying W=0 pairs leads to genuine
Superconducting Flux Quantization (SFQ). The data are understood in terms of a
cell-perturbation theory scheme which is very accurate for weak links. This
low-energy approach leads to an effective hard core boson Hamiltonian which
naturally describes itinerant pairs and SFQ in mesoscopic rings. For the
numerical calculations, we take advantage of a recently proposed exact
diagonalization technique which can be generally applied to many-fermion
problems and drastically reduces the size of the matrices to be handled.

Strongly Correlated Electrons