The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function ${\mathit{A}}_{\mathbf{p}}$ (\ensuremath{\omega}) is momentum dependent. Using ${\mathit{A}}_{\mathbf{p}}$ (\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.The self-energy of the hole-doped two-dimensional (2D) Hubbard model is calculated to second order in the interaction U and the ensuing renormalization of the spectral properties and of the Fermi surface is discussed. In uncorrelated systems the square-shaped Fermi surface separates the Fermi surface closed around the \ensuremath{\Gamma} point (with more holes than particles) from the Fermi surface closed around the Z point (with more particles than holes). In a correlated system a topological change from a Fermi surface centered around the \ensuremath{\Gamma} point to a Fermi surface closed around a Z point is induced, either by increasing the interaction or by diminishing the concentration of holes. The shape of the renormalized spectral function ${\mathit{A}}_{\mathbf{p}}$(\ensuremath{\omega}) is momentum dependent. Using ${\mathit{A}}_{\mathbf{p}}$(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.

Physical review. B, Condensed matterAug 1, 199525 citations

Spectral properties of two-dimensional Hubbard model with anisotropic hopping

V. Zlatić, P. Entel, S Grabowski

The zero-temperature spectral properties and Fermi surface (FS) anomalies of hole-doped 2D Hubbard model with anisotropic nearest-neighbor hopping are evaluated using the perturbation theory. The nested sections of the FS, which are always present in the anisotropic model, are found to expand with the strength of Coulomb correlation U. The renormalized FS and the low-energy part of the density of states obtained for small anisotropy and large U are similar to those obtained for large anisotropy and small U. The effect of correlation at low doping can best be described as an enhancement of the hopping anisotropy. The anomalous spectral features are mainly due to the van Hove singularities, which give rise to the momentum dependence of the self-energy.The zero-temperature spectral properties and Fermi surface (FS) anomalies of hole-doped 2D Hubbard model with anisotropic nearest-neighbor hopping are evaluated using the perturbation theory. The nested sections of the FS, which are always present in the anisotropic model, are found to expand with the strength of Coulomb correlation U. The renormalized FS and the low-energy part of the density of states obtained for small anisotropy and large U are similar to those obtained for large anisotropy and small U. The effect of correlation at low doping can best be described as an enhancement of the hopping anisotropy. The anomalous spectral features are mainly due to the van Hove singularities, which give rise to the momentum dependence of the self-energy.

Europhysics Letters (EPL)Jun 20, 199610 citations

{\mathit{A}}_{\mathbf{p}}

(\ensuremath{\omega}) is momentum dependent. Using

{\mathit{A}}_{\mathbf{p}}

(\ensuremath{\omega}) we evaluate dispersion of single-particle excitations. At low energies the band of quasiparticles with reduced bandwidth is clearly seen. At high energies and far away from the Fermi surface the spectra acquire an additional peak that describes excitations in the Hubbard band. The dispersion in Hubbard bands is weaker along the \ensuremath{\Gamma}-Z, than \ensuremath{\Gamma}-X or X-Z direction. The density of states of a correlated system, as given by the perturbation theory, remains logarithmically singular but the singular weight is reduced with respect to the uncorrelated one. In addition, the correlations transfer the spectral weight out of the low-energy region, where only a narrow Kondo-like structure seems to remain. The spectral properties of the 2D Hubbard model obtained by the truncated perturbation expansion resemble in many ways the recent experimental data on metallic cuprates.