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Physical review. B, Condensed matter

Nonconventional behavior of the one-band Hubbard Hamiltonian in two dimensions

J. Galán, F. Guinea, José Antonio Vergés, G. Chiappe, Enrique Louis

Published Aug 1, 1992• 14 citations
Publisher

Abstract

The wave-function renormalizaton constant Z has been calculated for the one-band Hubbard model in the square lattice. Near half-filling the Hamiltonian has been solved on finite clusters (up to 16\ifmmode\times\else\texttimes\fi{}16) by means of the unrestricted Hartree-Fock approximation, whereas at high dilutions (two electrons) exact calculations have been carried out. The region of the parameter space where the system shows nonconventional behavior (Z=0) is close to half-filling. For a given value of the Coulomb repulsion, Z vanishes at low dopings, and become finite as doping is increased. For very large U the constant Z remains finite for all dopings, excluding half-filling. These results are cast into a plausible phase diagram.

DOI
10.1103/physrevb.46.3163

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The wave-function renormalizaton constant Z has been calculated for the one-band Hubbard model in the square lattice. Near half-filling the Hamiltonian has been solved on finite clusters (up to 16\ifmmode\times\else\texttimes\fi{}16) by means of the unrestricted Hartree-Fock approximation, whereas at high dilutions (two electrons) exact calculations have been carried out. The region of the parameter space where the system shows nonconventional behavior (Z=0) is close to half-filling. For a given value of the Coulomb repulsion, Z vanishes at low dopings, and become finite as doping is increased. For very large U the constant Z remains finite for all dopings, excluding half-filling. These results are cast into a plausible phase diagram.
The wave-function renormalization constant Z has been calculated for the one-band Hubbard model on a square lattice. Near half-filling the Hamiltonian has been solved on finite clusters (up to 16\ifmmode\times\else\texttimes\fi{}16) by means of the unrestricted Hartree-Fock (UHF) approximation. Some checks of the UHF results have been made on 4\ifmmode\times\else\texttimes\fi{}4 clusters by means of the Lanczos method for U=\ensuremath{\infty}. At high dilutions (two electrons) exact calculations have been carried out. The ground-state wave functions and energies for the different cases here considered are discussed. The system shows nonconventional behavior (Z=0) near half-filling. For a given value of U, Z vanishes at low dopings, and becomes finite as doping is increased. For very large U the value of Z remains finite for all dopings, excluding half-filling. These results are cast into a plausible phase diagram.
The electron self-energy Sigma(k,\ensuremath{\omega}) corresponding to the one-band Hubbard Hamiltonian on clusters of the square lattice has been obtained as a function of the band filling up to second order in the interaction parameter U. The k dependence of the self-energy is completely taken into account. As a consequence, the imaginary part of the self-energy shows a linear behavior for fillings close to one electron per site whereas for large doping rates the quadratic \ensuremath{\omega} dependence characterizing Fermi liquids is recovered. The origin of this behavior has been investigated analytically: linear terms associated with nesting are shown to exist in any finite-dimensional lattice although its numerical relevance decreases very rapidly for space dimensionality larger than two. Implications of these results on the renormalization factor Z have been analyzed. From a practical point of view, we conclude that a standard second-order perturbative treatment is quantitatively precise for U values of the on-site Coulomb interaction smaller than the bandwidth of the noninteracting spectrum.
The ground-state wave function and energy are calculated for the one-band Hubbard Hamiltonian on a 4\ifmmode\times\else\texttimes\fi{}4 cluster of the square lattice up to first and second order of the on-site Coulomb repulsion U, respectively. Changes induced by a deviation of the number of electrons from half-filling (one electron per lattice site) are closely followed. Charge-charge and spin-spin correlation functions are directly obtained from the ground-state wave function and show the existence of antiferromagnetic correlations that extend over the whole cluster at half-filling. Correlations among sites separated by more than a lattice site diminish very rapidly as holes are introduced into the cluster. The analysis is extended to the negative-U case. Ground-state properties change qualitatively.
The Hubbard model in a two-dimensional square lattice is studied within the unrestricted Hartree-Fock approximation. A wide variety of solutions are found, as a function of filling and value of the Coulomb repulsion. Their properties range from those of magnetic polarons to a behavior similar to electrons in an external magnetic field (flux phases). The main features of the vortex solution are studied. It is shown that its energy increases logarithmically with system size, and that it becomes more stable for high values of the Coulomb repulsion and doping levels. Also, multivortex configurations are shown to exist. The implications of our results in the qualitative behavior of the Hubbard model as function of doping and strength of the interaction are discussed.
We have studied the two-dimensional Hubbard model on a square lattice with nearest-neighbor hopping. We first discuss the properties of the model within the mean-field approximation: Because of the form of the band structure, some peculiar features are found. We then discuss the simulation algorithm used and compare simulation results with exact results for 6-site chains to test the reliability of the approach. We present results for thermodynamic properties and correlation functions for lattices up to 8\ifmmode\times\else\texttimes\fi{}8 in spatial size. The system is found to be an antiferromagnetic insulator for all values of the coupling constant at zero temperature in the half-filled-band case, but the long-range order is much smaller than predicted by mean-field theory. We perform a finite-size-scaling analysis to determine the character of the transition at zero coupling. For non-half-filled-band cases, our results suggest that the system is always paramagnetic, in contradiction with Hartree-Fock predictions. The system does not show tendency to ferromagnetism nor triplet superconductivity in the parameter range studied. We also discuss some properties of the attractive Hubbard model in the half-filled-band case.
We consider the question of ferromagnetism in the one-band Hubbard model on the square lattice with infinite on-site repulsion using exact diagonalization techniques. Our results show a nonmonotonic behavior as a function of the number of holes Nh{N}_{h}Nh​ away from half filling. We find that the spin per electron is generally finite but less than its maximum value and, for a fixed hole number, increases with increasing system size. We interpret this as indicating that the inifinite-U Hubbard model is ferromagnetic in the thermodynamic limit for a finite fraction of holes, but that there are nonferromagnetic states which are very close in energy.