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Physical review. B, Condensed matter

Single-particle spectral weight of a two-dimensional Hubbard model

Elbio R. Dagotto, F. Ortolani, Douglas J. Scalapino

Published Aug 1, 1992• 97 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.46.3183

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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.
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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.
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.
Monte Carlo results for the frequency dependent conductivity ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$, the angular resolved photoemission spectral weight $A(\mathbf{p},\ensuremath{\omega})$, and the electron momentum distribution 〈np〉〈{n}_{\mathbf{p}}〉〈np​〉 are calculated for a half-filled Hubbard model with the on-site Coulomb interaction UUU equal to the bandwidth 8t8t8t. We find that even for U=8tU=8tU=8t, a spin-density-wave approximation provides a sensible description of this data and hence a useful picture of the electronic degrees of freedom in the insulating state.
Implementing an improved method for analytic continuation and working with imaginary-time correlation functions computed using quantum Monte Carlo simulations, we resolve the single-particle dispersion relation and the density of states (DOS) of the two-dimensional Hubbard model at half filling. At intermediate interactions of U/t=4,6U/t=4,6U/t=4,6, we find quadratic dispersion around the gap minimum at wave vectors $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ (the $\mathrm{\ensuremath{\Sigma}}$ points). We find saddle points at $\mathbf{k}=(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi},0),(0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi})$ (the XXX points), where the dispersion is approximately quartic, leading to a sharp DOS maximum above the almost flat ledge arising from the states close to $\mathrm{\ensuremath{\Sigma}}$. The fraction of quasiparticle states within the ledge is ${n}_{\mathrm{ledge}}\ensuremath{\approx}0.15$. Upon doping away from half filling, within the rigid-band approximation, these results support Fermi pockets around the $\mathrm{\ensuremath{\Sigma}}$ points, with states around the XXX points becoming filled only at doping fractions $x\ensuremath{\ge}{n}_{\mathrm{ledge}}$. The high density of states away from the $\mathrm{\ensuremath{\Sigma}}$ gap edge may be an important clue for a finite minimum doping level for superconductivity and other instabilities of doped Mott insulators.
The spectral weight A(p,\ensuremath{\omega}) of the two-dimensional t-J and Hubbard models has been calculated using exact diagonalization and quantum Monte Carlo techniques, at several densities 0.5\ensuremath{\le}〈n〉\ensuremath{\le}1.0. The photoemission (\ensuremath{\omega}0) region contains two dominant distinct features, namely a low-energy quasiparticle peak with bandwidth of order J, and a broad valence band peak at energies of order t. This behavior persists away from half-filling, as long as the antiferromagnetic correlations are robust. The results give support to theories of the copper oxide materials based on the behavior of holes in antiferromagnets, and they also provide theoretical guidance for the interpretation of experimental photoemission data for the cuprates.