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arXiv:cond-mat/9606142

Gutzwiller wave function under magnetic field

Hisatoshi Yokoyma, Shinya Tokizaki

Published Jun 19, 1996• 0 citations
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Abstract

Magnetization process of the Gutzwiller wave function is studied accurately by a variational Monte Carlo method. We apply it to the one-dimensional (1D) and 2D Hubbard models (HM), and to the 1D periodic Anderson model (PAM) without orbital degeneracy. For the HM, magnetization varies discontinuously to the full moment, as the magnetic field increases. For the PAM, the paramagnetic state is unstable against ferromagnetism, although the energy reduction thereof is small.

DOI
10.48550/arxiv.cond-mat/9606142

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Magnetization process of the Gutzwiller wave function is studied accurately by a variational Monte Carlo method. We apply it to the one-dimensional (1D) and 2D Hubbard models (HM), and to the 1D periodic Anderson model (PAM) without orbital degeneracy. For the HM, magnetization varies discontinuously to the full moment, as the magnetic field increases. For the PAM, the paramagnetic state is unstable against ferromagnetism, although the energy reduction thereof is small.
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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=1D=1D=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.
A new approach is presented for variational Monte Carlo simulations of Hubbard-Anderson models using Gutzwiller projection operators to restrict charge fluctuations in noninteracting wave functions. The Gutzwiller matrix elements are mapped onto a statistical model, which is evaluated using a stochastic algorithm that is normally applied to finite-temperature simulation. The method has been successfully tested for one-dimensional (1D) Hubbard and 1D Anderson models, and results are presented for the 2D Hubbard model. We find a region close to the half-filled limit where the Gutzwiller states of different magnetic ordering are very close in energy.
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The ground-state energy, hybridization energy, momentum distributions, local magnetic moments, and magnetic phase diagram of the symmetric periodic Anderson model are calculated using a correlated wave function in d=1,2, and 3 dimensions. The wave function is obtained by applying a Gutzwiller projector on a recently proposed single-particle product state with spin-density wave order. Evaluations are performed with an approximate scheme that becomes exact in high dimensions. Comparison with Monte Carlo data by Blankenbecler et al. for d=1 shows that the results are remarkably accurate for all values of the coupling. Hence the results for d=2,3 can be expected to be even more accurate and may serve as benchmarks for future numerical work in d>1.