https://doi.org/10.1140/epjb/e2004-00002-8
The 2-site Hubbard and
-
models
Dipartimento di Fisica “E.R. Caianiello” - Unità INFM di Salerno,
Università degli Studi di Salerno, 84081 Baronissi (SA),
Italy
Corresponding author: a avella@sa.infn.it
Received:
16
July
2003
Published online:
30
January
2004
The fermionic and bosonic sectors of the 2-site Hubbard model have
been exactly solved by means of the equation of motion and Green's
function formalism. The exact solution of the t-J model has
been also reported to investigate the low-energy dynamics. We have
successfully searched for the exact eigenoperators, and the
corresponding eigenenergies, having in mind the possibility to use
them as an operatorial basis on the lattice. Many local,
single-particle, thermodynamical and response properties have been
studied as functions of the external parameters and compared
between the two models and with some numerical and exact results.
It has been shown that the 2-site Hubbard model already contains
the most relevant energy scales of the Hubbard model: the local
Coulomb interaction U and the spin-exchange one . As a consequence of this, for some relevant
properties (kinetic energy, double occupancy, energy, specific
heat and entropy) and as regards the metal-insulator transition
issue, it has resulted possible to almost exactly mime the
behavior of larger systems, sometimes using a higher temperature
to get a comparable level spacing. The 2-site models have been
also used as toy models to test the efficiency of the Green's
function formalism for composite operators. The capability to
reproduce the exact solutions, obtained by the exact
diagonalization technique, gives a firm ground to the approximate
treatments based on this formalism.
PACS: 71.10.-w – Theories and models of many-electron systems / 71.10.Fd – Lattice fermion models (Hubbard model, etc.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003