https://doi.org/10.1140/epjb/e2002-00362-y
From independent particle towards collective motion for two polarized electrons on a square lattice
CEA/DSM, Service de Physique de l'État Condensé,
Centre d'Études de Saclay, 91191, Gif-sur-Yvette Cedex, France
Corresponding author: a pichard@drecam.saclay.cea.fr
Received:
28
March
2002
Published online:
19
November
2002
The two dimensional crossover from independent particle towards
collective motion is studied using 2 polarized electrons
(spinless fermions) interacting via a U/r Coulomb repulsion in
a 
square lattice with periodic boundary conditions and
nearest neighbor hopping t. Three regimes characterize the ground
state when U/t increases. Firstly, when the fluctuation 
of the spacing r between the two particles is larger than the lattice
spacing a, there is a scaling length 
such
that the relative fluctuation 
is a universal
function of the dimensionless ratio 
, up to finite size corrections of
order L-2. 
and 
are respectively the limits of
the free particle Fermi motion and of the correlated motion of a
Wigner molecule. Secondly, when U/t exceeds a threshold 
,
becomes smaller than a, giving rise to a correlated
lattice regime where the previous scaling breaks down and analytical
expansions in powers of t/U become valid. A weak random potential
reduces the scaling length and favors the correlated motion.
PACS: 71.10.-w – Theories and models for many-electron systems / 71.27.+a – Strongly correlated electron systems / 73.20.Qt – Electron solids
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002
