ELSEVIER Physica B 230-232 (1997) 466-468 Off-diagonal superconducting correlations and Nagaoka instability in the repulsive Hubbard model A.N. Kocharian a'u, A.K. Jermakian c'*, C. Yang d a Yerevan Institute of Physics, Yerevan, 375036 Armenia bDepartment of Physics, California State University Northridge, CA 91330-8268, USA CDepartment of Physics, New Jersey Institute of Technology, Newark, NJ 07102, USA d Graduate Institute of Physics Tamkang University, Tamsui 25137, Taiwan Abstract The finite Hubbard lattice with strong repulsion away from half-filling in a strong magnetic field is considered. The exact ground state energies and density-density correlation function for electrons in the high-spin limit with one spin-flip state (Nagaoka instability) is calculated for an arbitrary number of electrons and lattice sites in periodic hypercubes in one, two and three dimensions. The criteria for stability of either the spin-flipped phase or saturated Nagaoka state at large U and finite doping are derived. Keywords: Superconductivity; Nagaoka instability; Hubbard model The discovery of high-temperature supercon- ductivity in layered structure materials, like (VO)2P207 and Sr2Cu406 with weakly coupled arrays of metal-oxide-metal lattices, superconduc- tivity and ferromagnetism in fullerene systems, and the recent observation of strong superparamag- netism in certain small clusters of 4d atoms which do not exhibit ferromagnetism in the bulk, have increased interest in the problem of magnetism and superconductivity in highly correlated electron sys- tems [1]. We study here the ground-state properties and electron correlations in a finite size Hubbard lattice with periodic boundary conditions, away from half-filling and in the high-spin region (or in high applied magnetic field) near the Nagaoka instabil- ity I-2, 3] with one spin-flip [4, 5]. * Correspoding author. Let us consider the Hubbard hamiltonian with applied magnetic field B [6] H= --t ~ c -+ t,tr Cj,a q- U ~ FliTniT (i,j;,,~r i B 2 .~ ani,, (1) t,a which includes hopping terms between nearest- neighbor sites and intra-site repulsion (U > 0) for electrons with opposite spins. For simplicity we consider here the Hubbard model with a finite number of electrons N, where N t/d is integer on hypercubes with periodic bound- ary conditions in d dimension (linear size L TM inte- ger) for even number of atomic sites L (bipartite lattice) and odd numbers (nonbipartite). Notice that our periodic system has a particle-hole sym- metry only if the number of atomic sites is even (bipartite lattice). In a strong magnetic field the 0921-4526/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved PII S092 1-4526(96)006 1 6-3