https://doi.org/10.1140/epjb/e2004-00005-5
Fourth-order perturbation theory for the half-filled Hubbard model in infinite dimensions
1
Fachbereich Physik, Philipps-Universität Marburg,
35032 Marburg, Germany
2
Institut für Physik, Johannes-Gutenberg Universität Mainz,
55099 Mainz, Germany
3
Institut für Theoretische Physik III, Universität Stuttgart,
70550 Stuttgart, Germany
Corresponding author: a florian.gebhard@physik.uni-marburg.de
Received:
17
June
2003
Revised:
9
September
2003
Published online:
30
January
2004
We calculate the zero-temperature self-energy
to fourth-order perturbation theory in the Hubbard interaction U
for the half-filled Hubbard model in infinite dimensions.
For the Bethe lattice with bare bandwidth W,
we compare our perturbative results for the self-energy,
the single-particle density of states, and the momentum
distribution to those from
approximate analytical and numerical studies of the model.
Results for the density of states from perturbation theory
at U/W=0.4 agree very well with those from
the Dynamical Mean-Field Theory treated with
the Fixed-Energy Exact Diagonalization and
with the Dynamical Density-Matrix Renormalization Group.
In contrast, our results reveal the limited resolution of
the Numerical Renormalization Group approach in treating
the Hubbard bands.
The momentum distributions from all approximate studies of the model
are very similar in the regime where perturbation theory
is applicable, 
. Iterated Perturbation Theory
overestimates the quasiparticle weight above
such moderate interaction strengths.
PACS: 71.10.Fd – Lattice fermion models (Hubbard model, etc.) / 71.27.+a – Strongly correlated electron systems; heavy fermions / 71.30.+h – Metal-insulator transitions and other electronic transitions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003
