Phys. Rev. B 46, 11779 (1992)

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Density of states of the two-dimensional Hubbard model on a 4 x 4 lattice

P. W. Leung

Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4052

Zhiping Liu and Efstratios Manousakis

Department of Physics and Center for Materials Research and Technology
Supercomputer Computations Research Institute Florida State University, Tallahassee, Florida 32306

M. A. Novotny

Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4052

Paul E. Oppenheimer

Thinking Machines Corporation, Cambridge, Massachusetts 02142-1264

Using exact diagonalization, we calculate the density of states of the two-dimensional Hubbard model on a 4 x 4 square lattice at U/t=0.5, 4, and 10, and even number of electrons with filling factors n ranging from a quarter filling up to half filling. We compare the ground-state energy and density of states at U/t=0.5 and 4 with second-order perturbation theory in U/t in the paramagnetic phase, and find that while the agreement is reasonable at U/t=0.5, it becomes worse as the perturbatively determined (i.e., using Stoner's criterion) boundary of the paramagnetic to spin-density-wave instability is approached. In the strong coupling regime (U/t=10), we find reasonable agreement between the density of states of the Hubbard and the t-J model especially for low doping fractions. In general, we find that at half filling the filled states are separated from the empty states by a gap. At U/t=10, the density of states shows two bands clearly separated by a Mott-Hubbard gap of order U.

©1992 The American Physical Society.

PACS: 74.20.-z

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