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Physical review. B, Condensed matter

Quasiparticle spectral density of low-dimensional Hubbard Hamiltonians

A. Martín‐Rodero, Enrique Louis, Fernando Flores, C. Tejedor

Published Jan 1, 1984• 16 citations
Publisher

Abstract

The spectral density of states of one- and two-dimensional Hubbard Hamiltonians is analyzed by means of Green's-function techniques. The procedure has been checked in the half-filled---band one-dimensional case by comparing it with the well-known solution of Lieb and Wu. When the ratio between the intrasite Coulomb interaction and the transfer integral is great enough, we find for subbands for both the one- and two-dimensional cases. Implications for Si(111) surfaces are commented on.

DOI
10.1103/physrevb.29.476

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The spectral density of states of one- and two-dimensional Hubbard Hamiltonians is analyzed by means of Green's-function techniques. The procedure has been checked in the half-filled---band one-dimensional case by comparing it with the well-known solution of Lieb and Wu. When the ratio between the intrasite Coulomb interaction and the transfer integral is great enough, we find for subbands for both the one- and two-dimensional cases. Implications for Si(111) surfaces are commented on.
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.
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.
The two-dimensional Hubbard model on the square lattice is studied in the presence of lattice distortions in the adiabatic approximation. The self energy is computed within perturbation theory up to second order, which provides a way for studying the quasiparticle dispersion. We compute numerically the second order contribution to the self-energy using a standard Fast Fourier Transform Algorithm for finite system sizes. The stability of the lattice distortions is investigated and a schematic phase diagram is drawn. The Fermi surface is analyzed for densities near to half filling, the presence of lattice distortion change some spectral properties of the model and gives an anisotropic interacting FS. The spectral function is calculated along several lines in momentum space and the renormalized quasiparticle dispersion is obtained. The behavior of the density of states is shown for different values of the intrasite repulsion U in the different phases.
We investigate the ground state (T = 0 K) of the one-dimensional symmetrical (n = 1) Hubbard model formalized in terms of the system of integral equations, which we previously obtained using the method of the generating functional of Green’s functions with the subsequent Legendre transformation. In a wide range of variations in the parameter of Coulomb interaction U, the following characteristics of the system have been calculated: the electron density of states, the electron band spectrum, the number of doubly occupied lattice sites, the localized magnetic moment, the correlator of the square of the longitudinal component of spin at a site,<S Z 2>, and the internal energy of the system. It has been shown that, for all U > 0, the model yields two solutions, i.e., an antiferromagnetic insulator and a paramagnetic insulator, in which there are no single-electron quasi-particles at the Fermi level. The energy of the paramagnetic solution in the region of U < 1.1 is considerably less than that of the antiferromagnetic solution for the case of U > 1.1, we have the opposite situation.
Electronic states of a two-dimensional Hubbard model near half filling is investigated by use of the composite-operator method, which is improved by including two-site correlations in combined use with the resolvent method. The densities of states obtained for the upper and lower Hubbard bands have three-peek structures at half filling and give shapes above a certain temperature similar to the ones obtained in the numerical simulation by Dagotto, Ortolani, and Scalapino [Phys. Rev. B 46, 3183 (1992)], but show narrowing of the bands at low temperature due to the formation of spin-singlet states among the nearest-neighbor electrons. A doped case shows a coherent peak at the Fermi level and the feature of the density of states is very similar to the one from numerical simulation. The one-particle spectra in the (k,k) direction is also presented. The results show that, at half filling, the spectral weight is not evenly distributed between two bands; most of the weight of the lower Hubbard band appears between (0,0) and (\ensuremath{\pi}/2a,\ensuremath{\pi}/2a), while that of the upper Hubbard band lies in the region between (\ensuremath{\pi}/2a,\ensuremath{\pi}/2a) and (\ensuremath{\pi}/a,\ensuremath{\pi}/a), keeping roughly the original band distribution. With hole doping, a flat band develops at the Fermi level with a large Fermi surface and the lower Hubbard band extends through the whole Brillouin zone.
A pair theory of the Hubbard Hamiltonian is presented for the case of a half-filled band. The original Hamiltonian is reformulated exactly in terms of pair operators which satisfy boson commutation relations. The pair energies and wave functions are obtained explicitly. In the one-dimensional case, these reduce to the results derived by Lieb and Wu for M=1M=1M=1. The pair Hamiltonian offers a better starting point for perturbation treatments or variational calculations.