The Nagaoka instability and off-diagonal superconductivity in the finite Hubbard lattice

The first strict evidence for time-reversal symmetry breaking and change in statistics of electrons in U(1) gauge field, induced by periodic boundary conditions is demonstrated for 1d Hubbard model with U→∞. The exact ground state energy, eigenfunction and one-particle density correlation function are calculated for arbitrary number of electrons and lattice sites. The criteria for the stability of either the Nagaoka state or spontaneously broken superconducting state with off-diagonal long-range order are found. The theory predicts the existence of superconductivity and ferromagnetism for electrons in periodic lattices and mesoscopic rings. The electrons in lattices are shown to provide for the presence of parity-dependent paramagnetic and diamagnetic persistent currents in the ground state