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Physical review. B, Condensed matter

Numerical study of the spectral weight function for the half-filled two-dimensional Hubbard model

G. S. Feng, Steven R. White

Published Oct 1, 1992• 13 citations
Publisher

Abstract

The spectral weight function A(p,\ensuremath{\omega}) and density of states D(\ensuremath{\omega}) at half filling are calculated with an exact diagonalization technique on the 4\ifmmode\times\else\texttimes\fi{}4 square lattice in the one-band Hubbard model from weak to strong coupling. Quasiparticle peaks are observed at weak and moderate couplings, while mostly incoherent structure appears at strong coupling. The gap in the density of states can be observed for all couplings and widens as the interaction strength increases.

DOI
10.1103/physrevb.46.8691

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The spectral weight function A(p,\ensuremath{\omega}) and density of states D(\ensuremath{\omega}) at half filling are calculated with an exact diagonalization technique on the 4\ifmmode\times\else\texttimes\fi{}4 square lattice in the one-band Hubbard model from weak to strong coupling. Quasiparticle peaks are observed at weak and moderate couplings, while mostly incoherent structure appears at strong coupling. The gap in the density of states can be observed for all couplings and widens as the interaction strength increases.
The spectral function of a single hole in the two-dimensional Hubbard model is studied numerically through exact diagonalization for a nine-site cluster over a wide range of interaction strengths U. In the weak-interaction limit, the spectral function consists of sharp quasiparticle peaks corresponding to the allowed single-particle excitations of the noninteracting system. As the interaction strength increases, the spectral weight begins to spread over a large range of energies, and satellite structures appear at higher excitation energy. The band-narrowing effect and the quasiparticle weight are investigated. The results are discussed in connection with other analytical and numerical studies on the spectral function.
We report the results of a calculation of the spectral weight function of a single hole (or electron) placed in an otherwise half-filled band described by the one-orbital Hubbard model. The calculation is made by exact diagonalization. An eight-site cubic cluster is considered. The density of states is studied as the interaction strength is varied between weak and strong couplings. We observe the spreading of the spectral weight associated with some single-particle eigenstates over a large range of energies, and the appearance of satellite structure at higher excitation energies. Only modest band narrowing is found.
Numerical results for the single-particle spectral weight A(p,\ensuremath{\omega}) and the density of states N(\ensuremath{\omega}) for a 4\ifmmode\times\else\texttimes\fi{}4 Hubbard model are presented. Both the half filled insulating state and the doped metallic state are considered. At half filling the numerical results are compared with the mean-field spin-density-wave single-particle spectral weight, and away from half filling with a renormalized quasiparticle band description. The relationship of these results to experimental photoemission, inverse photoemission, and angular-resolved measurements is discussed.
Using exact diagonalization, we calculate the density of states of the two-dimensional Hubbard model on a 4\ifmmode\times\else\texttimes\fi{}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.
We have calculated the single-particle density of states N(\ensuremath{\omega}) and the spectral weight A(p,\ensuremath{\omega}) for the doped two-dimensional Hubbard model by combining quantum Monte Carlo simulations with the maximum-entropy analytic continuation technique. We present results for various values of the doping, temperature, and Coulomb repulsion U. For sufficiently strong Coulomb repulsions and near half filling, a Mott-Hubbard pseudogap exists. In this case, we find that a peak develops at the top of the lower Hubbard band near the Fermi level at temperatures of order of the hopping t. The structure of this peak is similar to that seen in the infinite dimensional Hubbard model.