https://doi.org/10.1140/epjb/e2003-00266-4
Analytical and numerical treatment of the Mott–Hubbard insulator in infinite dimensions
1
Department
of Chemistry and Biochemistry, University of California,
La Jolla, CA 92093-0371, USA
2
Fachbereich Physik, Philipps-Universität Marburg,
35032 Marburg, Germany
3
Institut für Theoretische Physik III, Universität Stuttgart,
70550 Stuttgart, Germany
Corresponding author: a florian.gebhard@physik.uni-marburg.de
Received:
5
March
2003
Revised:
14
July
2003
Published online:
2
October
2003
We calculate the density of states in the half-filled
Hubbard model on a Bethe lattice with infinite connectivity.
Based on our analytical results to second order in t/U,
we propose a new `Fixed-Energy Exact Diagonalization' scheme
for the numerical study of the Dynamical Mean-Field Theory.
Corroborated by results from the Random Dispersion Approximation,
we find that the gap opens at 
.
Moreover, the density of states near the gap increases algebraically
as a function of frequency with an exponent 
in the
insulating phase. We critically examine other analytical
and numerical approaches
and specify their merits and limitations
when applied to the Mott–Hubbard insulator.
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
