Article

Exact ground states for the four-electron problem in a two-dimensional Hubbard square system

Philosophical Magazine (Impact Factor: 1.6). 05/2006; 86(13-14):2073. DOI: 10.1080/14786430500070347
Source: arXiv

ABSTRACT We present exact explicit analytical results describing the exact ground
state of four electrons in a two-dimensional square Hubbard cluster
containing 16 sites taken with periodic boundary conditions. The
presented procedure, which works for arbitrary even particle number and
lattice sites, is based on explicitly given symmetry adapted base
vectors constructed in r space. The Hamiltonian acting on these states
generates a closed system of 85 linear equations, providing by its
minimum eigenvalue, the exact ground state of the system. The presented
results, described with the aim to generate further creative
developments, not only show how the ground state can be exactly obtained
and what kind of contributions enter in its construction, but also
emphasize further characteristics of the spectrum. On this line (i)
possible explications are found regarding why weak coupling expansions
often provide a good approximation for the Hubbard model at intermediate
couplings, or (ii) explicitly given low-lying energy states of the
kinetic energy, avoiding double occupancy, suggest new roots for pairing
mechanism attracting decrease in the kinetic energy, as emphasized by
kinetic energy driven superconductivity theories.

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