https://doi.org/10.1007/PL00011095
Pairing mechanism in the doped Hubbard antiferromagnet: the 4x4 model as a test case
Istituto Nazionale di Fisica della Materia, Dipartimento di Fisica,
Universita' di Roma Tor Vergata, Via della Ricerca Scientifica, 1-00133
Roma, Italy
Corresponding author: a cini@roma2.infn.it
Received:
24
October
2000
Published online: 15 March 2001
We introduce a local formalism, in terms of eigenstates of number
operators, having well defined point symmetry, to solve the Hubbard model
at weak coupling on a square lattice (for even N).
The key concept is that of W=0 states, that are the many-body
eigenstates of the kinetic energy with
vanishing Hubbard repulsion. At half filling, the wave function
demonstrates an antiferromagnetic order, a lattice step translation
being equivalent to a spin flip. Further,
we state a general theorem which allows to find all the
W=0 pairs (two-body W=0 singlet states).
We show that, in special cases, this assigns the ground
state symmetries at least in the weak coupling regime.
The N=4 case is discussed in detail. To study the doped half filled system,
we enhance the group theory analysis of the
Hubbard model introducing an Optimal Group which
explains all the degeneracies in the one-body and many-body spectra.
We use the Optimal Group to predict the possible ground state symmetries
of the
doped antiferromagnet by means of our general theorem
and the results are in agreement with exact diagonalization data.
Then we create W=0
electron pairs over the
antiferromagnetic state. We show analitycally that the effective interaction
between the electrons of the pairs is attractive and forms
bound states. Computing the corresponding binding energy we are able to definitely
predict the exact ground state symmetry.
PACS: 74.20.Mn – Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.) / 71.10.Li – Excited states and pairing interactions in model systems / 74.72.-h – High-Tc compounds
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001