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.

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: An exact analytical diagonalization is used to solve the two dimensional Extended Hubbard Model for system with finite size. We have considered an Extended Hubbard Model (EHM) including on-site and off-site interactions with interaction energy U and V respectively, for square lattice containing 4*4 sites at one-eighth filling with periodic boundary conditions, recently treated by Kovacs et al [1]. Taking into account the symmetry properties of this square lattice and using a translation linear operator, we have constructed a r-space basis, only, with 85 state-vectors which describe all possible distributions for four electrons in the 4*4 square lattice. The diagonalization of the 85*85 matrix energy allows us to study the local properties of the above system as function of the on-site and off-site interactions energies, where, we have shown that the off-site interaction encourages the existence of the double occupancies at the first exited state and induces supplementary conductivity of the system.
    Physica Scripta 10/2011; 78(2). · 1.03 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: A technique based on the transformation in positive semidefinite form of the Hamiltonian (Ĥ) is developed to allow the study of the enlargement possibilities of the emergence domain of a given state. For this reason the calculation of exact ground states for the polyphenylene type of non-integrable chains is performed. Using different exact transcriptions of Ĥ in positive semidefinite form and different solutions of the matching equations, the same type of ground state is deduced in different regions of the parameter space, hence a more global view of its emergence possibilities is obtained. With this procedure an enlarged view of the appearance in the phase diagram of different studied phases can be achieved.
    Philosophical Magazine A 12/2012; 92(36):4657-4675.

Full-text (2 Sources)

Available from
May 28, 2014