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Physical review. B, Condensed matter

Gutzwiller-Jastrow wave functions for the 1/rHubbard model

D. F. Wang, Q. F. Zhong, Piers Coleman

Published Sep 15, 1993• 18 citations
Publisher

Abstract

In this work, we study the wave functions of the one-dimensional 1/r Hubbard model in the strong-interaction limit U=\ensuremath{\infty}. A set of Gutzwiller-Jastrow wave functions are shown to be eigenfunctions of the Hamiltonian. The entire excitation spectrum and the thermodynamics are also studied in terms of more generalized Jastrow wave functions. For the wave functions and integrability conditions at finite on-site energy, further investigations are needed.

DOI
10.1103/physrevb.48.8476

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In this work, we study the wave functions of the one-dimensional 1/r Hubbard model in the strong-interaction limit U=\ensuremath{\infty}. A set of Gutzwiller-Jastrow wave functions are shown to be eigenfunctions of the Hamiltonian. The entire excitation spectrum and the thermodynamics are also studied in terms of more generalized Jastrow wave functions. For the wave functions and integrability conditions at finite on-site energy, further investigations are needed.
Gutzwiller-Jastrow Wavefunctions for the 1/r1/r1/r Hubbard Model
In this work, we study the wavefunctions of the one dimensional 1/r1/r1/r Hubbard model in the strong interaction limit U=∞U =\inftyU=∞. A set of Gutzwiller-Jastorw wavefunctions are shown to be eigen-functions of the Hamiltonian. The entire excitation spectrum and the thermodynamics are also studied in terms of more generalized Jastrow wavefunctions. For the wavefunctions and integrability conditions at finite on-site energy, further investigations are needed.
In this work we introduce a one-dimensional multiple-component Hubbard model with 1/r hopping and on-site energy U. The wave functions, the spectrum, and the thermodynamics are studied for this model in the strong-interaction limit U\ensuremath{\rightarrow}\ensuremath{\infty}. In this limit, the system is a special example of SU(N) Luttinger liquids, exhibiting spin-charge separation in the full Hilbert space. Speculations on the physical properties of the model at finite on-site energy are also discussed.
One dimensional chiral Hubbard model reduces to the Haldane-Shastry spin chain at half-filling with large but finite on-site energy UUU.In this talk, we show that the Gutzwiller-Jastrow wavefunctions are the eigen-states of the Hubbard model at U=+∞U=+\inftyU=+∞ at less than half-filling. The full energy spectrum and an infinite set of mutually commuting constants of motion are also given in this limit for the system.
We introduce a new lattice version of the correlated-basis-function approach for the study of strongly interacting electrons. As a first application we have chosen the one-dimensional Hubbard model. For this system, we have implemented different types of correlations: namely, (a) Gutzwiller; (b) Jastrow; (c) nearest-neighbor spin-spin; (d) excitonic (e-d); and (f) pairing (BCS). The resulting energies, momentum distribution, and other quantities are compared with exact results (when available) and are discussed, both from the methodological and physical point of view. The most important correlations that are needed to obtain good ground-state energies are found to be Gutzwiller (reduced double occupancy) plus e-d correlations (between empty and doubly occupied sites), in agreement with other studies.
New variational wave functions are introduced to describe the Hubbard model in strong correlation. Intersite correlation (or Jastrow) factors are taken into account beyond the Gutzwiller wave function (GF). A study is made on the one-dimensional lattice and the two-dimensional square lattice at half-filling as well as less-than-half-filling. Much improvement can be achieved thereby in the description of physical quantities such as the momentum distribution and spin and charge density correlation functions. In addition, the ground state energy is lowered appreciably compared with the GF. In this connection, the Mott-Hubbard-type metal-insulator transition is also re-examined.
Exact relations are derived for the Fermi Hubbard spectral weight function for infinite U at zero temperature in the thermodynamic limit for any dimension,any lattice structure and general hopping matrix. These relations involve moments of the spectral weight function but differ from similar work by (a) restricting the moments over the interesting low energy (lower Hubbard band) spectrum and (b) without any of the usual approximations (e.g. decoupling) for the requisite higher order correlation functions. The latter are determined exactly as explicit functions of the single particle correlation function in the infinite U limit. The methods behind these results have the additional virtue of simplicity - cumbersome, but entirely straightforward. In a companion paper, the relations offer rich insights into the model behavior and offer severe tests - a computer lab - of any proposed solution to the Hubbard model in the strong correlation (large finite U) region. As the electron density approaches one electron per site, then the correlation functions become local, so are trivial to compute exactly. In that limit and for the paramagnetic case, the second central moment of the spectral weight function is not zero, but quite large.