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Physical Review Letters

One-electron spectral weight of the doped two-dimensional Hubbard model

Niyazi Bulut, Douglas J. Scalapino, Steven R. White

Published Jan 31, 1994• 100 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.72.705

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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.
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.
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Abstract Using the strong-coupling diagram technique, low-temperature spectral properties of the two-dimensional fermionic Hubbard model are considered for strong and moderate Hubbard repulsions U . The electron hopping to the nearest, second and third neighbors is taken into account with hopping constants t , t ′ = − 0.3 t and t ″ = 0.2 t , respectively. The nonzero values of t ′ and t ″ lead to strong asymmetry in magnetic properties with respect to the hole and electron doping—for U = 8 t strong antiferromagnetic correlations are retained up to the electron concentration n ¯ ≈ 1.25 , while they are destroyed completely at n ¯ ≈ 0.87 . When the temperature is decreased to T ≲ 0.1 t , in a wide range of electron concentrations there appear narrow and intensive peaks at the Fermi level (FL) in densities of states. For U ≲ 6 t the peaks are seen even at half-filling, while for larger U they arise as the FL leaves the Mott gap. The peaks are connected with a narrow band emerging at low temperatures. We identify states forming the band with spin-polaron excitations—bound states of correlated electrons and mobile spin excitations. Obtained low-temperature spectral functions are used for interpreting the peak-dip-hump structure observed in the photoemission of Nd 2− x Ce x CuO 4 . In the case of hole doping, the calculated Fermi contour contains arcs near nodal points with pseudogaps near antinodal points, while for electron doping the spectral intensity is suppressed at hot spots, in agreement with experimental observations in cuprate perovskites.
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 investigate the dynamical properties of the one-dimensional Hubbard model using the quantum Monte Carlo method and the numerical analytic continuation method based on the maximum entropy principle. Results for the spin, charge and current excitation spectrum are presented for various values of the coupling and the band filling for the system of 24 sites with the periodic boundary condition. We find that the total spectral density of the spin excitation exhibits a gapless structure irrespective of the coupling or the band filling. The charge excitation spectrum, on the other hand, clearly shows the gap formation at the half filled band and shifts its weight toward the higher energy region with increase of the coupling. This charge excitation gap, however, disappears with the hole doping. We also discuss the momentum dependence of the spectral functions.