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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
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