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Physical review. B, Condensed matter

Spectral weight function for the two-dimensional Hubbard model

Steven R. White

Published Sep 1, 1991• 85 citations
Publisher

Abstract

We present results for the single-particle spectral weight function for the two-dimensional Hubbard model. Results were obtained using analytic expressions for the first two moments of the spectral weight function, along with numerical calculations using a combination of quantum Monte Carlo and the maximum-entropy method of analytic continuation. The expressions for the first two moments are surprisingly simple, involving only the parameters of the model, the chemical potential, and the filling. At half-filling, the squared width (variance) of the spectral weight is exactly ${\mathit{U}}^{2}$/4. Numerical results are shown for 8\ifmmode\times\else\texttimes\fi{}8 lattices at a variety of fillings and momenta. The insulating antiferromagnetic gap in the spectral weights, readily apparent in the results at half-filling, is absent at a filling of 0.95.

DOI
10.1103/physrevb.44.4670

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We present results for the single-particle spectral weight function for the two-dimensional Hubbard model. Results were obtained using analytic expressions for the first two moments of the spectral weight function, along with numerical calculations using a combination of quantum Monte Carlo and the maximum-entropy method of analytic continuation. The expressions for the first two moments are surprisingly simple, involving only the parameters of the model, the chemical potential, and the filling. At half-filling, the squared width (variance) of the spectral weight is exactly U2{\mathit{U}}^{2}U2/4. Numerical results are shown for 8\ifmmode\times\else\texttimes\fi{}8 lattices at a variety of fillings and momenta. The insulating antiferromagnetic gap in the spectral weights, readily apparent in the results at half-filling, is absent at a filling of 0.95.
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.
Using a combination of quantum Monte Carlo and the maximum-entropy method, we have studied the formation of gaps and pseudogaps in the single-particle spectral weight function A(p,\ensuremath{\omega}) for the two-dimensional half-filled Hubbard Model. We present results for U/t=4 from lattices ranging from 4\ifmmode\times\else\texttimes\fi{}4 to 16\ifmmode\times\else\texttimes\fi{}16, and for inverse temperatures ranging from \ensuremath{\beta}=2 to \ensuremath{\beta}=12. We find that a pseudogap appears only when the spin-spin correlations are comparable to the size of the lattice. Since the spin-spin correlation length is known to diverge only at T=0, the implication is that in an infinite lattice there is no pseudogap except at T=0 for U/t=4.
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.
Dynamic properties of the three-dimensional single-band Hubbard model are studied using quantum Monte Carlo combined with the maximum entropy technique. At half-filling, there is a clear gap in the density of states and well-defined quasiparticle peaks at the top (bottom) of the lower (upper) Hubbard band. We find an antiferromagnetically induced weight above the naive Fermi momentum. Upon hole doping, the chemical potential \ensuremath{\mu} moves to the top of the lower band where a robust peak is observed. Results are compared with spin-density-wave mean-field and self-consistent Born approximation results, and also with the infinite-dimensional (D=\ensuremath{\infty}) Hubbard model, and experimental photoemission for three-dimensional transition-metal oxides. \textcopyright{} 1996 The American Physical Society.
Using grand canonical quantum Monte Carlo (QMC) simulations combined with maximum entropy analytic continuation, as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at half-filling. The one-particle spectral weight function, A(k,\ensuremath{\omega}), undergoes a qualitative change with interchain hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ associated with a transition from a four-band insulator to a two-band insulator. A simple analytical model based on the propagation of exact rung singlet states gives a good description of the features at large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. For smaller ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$, A(k,\ensuremath{\omega}) is similar to that of the one-dimensional model, with a coherent band of width the effective antiferromagnetic exchange J which is reasonably well described by renormalized spin-wave theory. The coherent band rides on a broad background of width several times the parallel hopping integral t, an incoherent structure similar to that found in calculations on both the one- and two-dimensional models. We also present QMC results for the two-particle spin and charge excitation spectra, and relate their behavior to the rung singlet picture for large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and to the results of spin-wave theory for small ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. \textcopyright{} 1996 The American Physical Society.