Annalen der Physik

Variational approach to spin fluctuations in the Hubbard model

S. Dahm, W. Brenig

Published Jan 1, 1995• 0 citations

Abstract

Abstract We study a one parameter variational wave function to improve the spin density wave ground state of the Hubbard model by inclusion of quantum spin fluctuations. Using a perturbative approach and novel lattice summation techniques we present analytical as well as numerical results for the correlation energies and the staggered magnetizations in one and two dimensions. We find ground state energies which are satisfyingly close to known exact results and are significantly lower than those of existing Gutzwiller and numerical treatments.

DOI: 10.1002/andp.19955070703

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Annalen der Physik

Variational approach to spin fluctuations in the Hubbard model

S. Dahm, W. Brenig

Published Jan 1, 1995• 0 citations

Publisher

Abstract

DOI: 10.1002/andp.19955070703

Related papers

High-order perturbation expansion for the two-dimensional Hubbard model using the Gutzwiller wave function

Zsolt Gulácsi, M. Gulácsi, Boldizsár Jankó

A variational approach of the two-dimensional Hubbard model is presented, based on the Gutzwiller wave function, making no use of the Gutzwiller approximation. We calculated exactly the coefficients of the ( ${\mathit{g}}^{2}$ -1 ${)}^{\mathit{m}}$ expansion of the ground-state energy (g is the Gutzwiller variational parameter) up to the m=8 order. The m>8 terms were deduced with an acuracy O[(n/2 ${)}^{18}$ ] as a function of the electron concentration n. Double occupancy, expectation value of the interaction energy, average kinetic energy, and the minimized ground-state energy are determined and their electron concentration and dimensionality dependence are discussed. An evaluation of the nonanalyticities for any dimension is also presented.A variational approach of the two-dimensional Hubbard model is presented, based on the Gutzwiller wave function, making no use of the Gutzwiller approximation. We calculated exactly the coefficients of the (${\mathit{g}}^{2}$-1${)}^{\mathit{m}}$ expansion of the ground-state energy (g is the Gutzwiller variational parameter) up to the m=8 order. The m>8 terms were deduced with an acuracy O[(n/2${)}^{18}$] as a function of the electron concentration n. Double occupancy, expectation value of the interaction energy, average kinetic energy, and the minimized ground-state energy are determined and their electron concentration and dimensionality dependence are discussed. An evaluation of the nonanalyticities for any dimension is also presented.

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arXiv:cond-mat/0111043Physical review. B, Condensed matterApr 12, 200218 citations

{\mathit{g}}^{2}

-1

{)}^{\mathit{m}}

expansion of the ground-state energy (g is the Gutzwiller variational parameter) up to the m=8 order. The m>8 terms were deduced with an acuracy O[(n/2

{)}^{18}

] as a function of the electron concentration n. Double occupancy, expectation value of the interaction energy, average kinetic energy, and the minimized ground-state energy are determined and their electron concentration and dimensionality dependence are discussed. An evaluation of the nonanalyticities for any dimension is also presented.

{n}_{\mathrm{k}}

and ground-state energy E for arbitrary density n and interaction strength U. In the case of a half-filled band and large U, hitherto unexpected nonanalyticities are found. The results allow for the first approximation-free assessment of the properties of the Gutzwiller wave function. It is shown that the well-known Gutzwiller approximation may be derived diagrammatically, too. The approximation is seen to yield the exact results for expectation values in terms of this wave function in the limit of infinite dimensionality.

We present analytic results for ground-state properties of Hubbard-type models in terms of the Gutzwiller variational wave function with nonzero values of the magnetization m. In dimension

D=1

approximation-free evaluations are made possible by appropriate canonical transformations and an analysis of umklapp processes. We calculate the double occupation and the momentum distribution, as well as its discontinuity at the Fermi surface, for arbitrary values of the interaction parameter g, density n, and magnetization m. These quantities determine the expectation value of the one-dimensional Hubbard Hamiltonian for any symmetric, monotonically increasing dispersion ${\ensuremath{\epsilon}}_{k}.$ In particular for nearest-neighbor hopping and densities away from half filling the Gutzwiller wave function is found to predict ferromagnetic behavior for sufficiently large interaction U.