Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Accurate variational results for the symmetric periodic Anderson model in one, two, and three dimensions

Zsolt Gulácsi, Rainer Strack, D. Vollhardt

Published Apr 1, 1993• 22 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.47.8594

Related papers

NEW VARIATIONAL APPROACH TO THE PERIODIC ANDERSON MODEL WITH ANTIFERROMAGNETIC ORDER

Rainer Strack, D. Vollhardt

We propose a new variational wave function for the periodic Anderson model in the case of antiferromagnetically ordered f-electrons. Expectation values in terms of this wave function can be calculated analytically in arbitrary dimensions d. The wave function automatically produces the exact limiting behavior of the ground state energy for weak hybridization and strong f-electron interaction in the symmetric case, which the Gutzwiller wave function fails to do. Several additional improvements are discussed. Thereby one obtains a wave function that leads to extremely good ground state energies for the periodic Anderson model for arbitrary U in all dimensions d.

Modern Physics Letters B•Aug 30, 1991•9 citations

A variational treatment of the periodic Anderson model with antiferromagnetic order

W. Brenig, E. Müller‐Hartmann

Abstract We discuss a variational ground state wave function for the symmetric periodic Anderson model with commensurate spin density order. The energy of this ansatz is evaluated in closed form. Our approach generalizes a variational treatment proposed recently by Strack and Vollhardt and results in significantly lower energy. Contrary to the Gutzwiller ansatz the wave function recovers the Schrieffer‐Wolff limit for large Coulomb repulsion. We clarify the relation of our approach to unrestricted Hartree‐Fock and present a comparison with existing quantum Monte Carlo calculations for one dimension.

Annalen der Physik•Jan 1, 1992•3 citations

Equivalence of variational and slave-boson mean-field treatments of the periodic Anderson model

Florian Gebhard

We investigate Gutzwiller-correlated wave functions as variational ground states for the periodic Anderson model. We extend a recently developed technique for the Hubbard model to the case of two hybridized bands with degeneracy N. We calculate expectation values in the following limits: dilute system (single-impurity case), large degeneracy N, and large dimension d. The mean-field results using the slave-boson approach of Coleman and of Kotliar and Ruckenstein are reproduced in the large-N and large-d limit, respectively. These techniques, therefore, obey variational principles at T=0 in the respective limits and their applicability for T>0 is naturally limited to the Fermi-liquid regime. Evaluations of Gutzwiller-correlated wave functions using the ``Gutzwiller approximation'' are seen to become exact in the limit of large dimensions. A systematic expansion in 1/d can be performed for N=2. In general, corrections are small, of order 1/(dN).

Physical review. B, Condensed matter•Jul 15, 1991•35 citations

Alternative to Gutzwiller’s approach

Sushil Lamba, S. K. Joshi

An efficient variational procedure to calculate the ground-state properties of the particle-hole symmetric periodic Anderson model is presented. Expectation values are calculated by using an approximate scheme. It is shown that the ground-state energy calculated with the one-site approximation, which essentially is a single-site mean-field approximation, is identical to the corresponding energy obtained by the well-known Gutzwiller wave function using the Gutzwiller approximation. The two-site approximation, in which intersite correlations are explicitly included, is shown to be a better approximation than the Gutzwiller approximation.

Physical review. B, Condensed matter•Sep 15, 1995•2 citations

Wave Functions of Correlated-Electron State in the Periodic Anderson Model

Takashi Yanagisawa

We investigate the periodic Anderson model by a variational Monte Carlo method. A new wave function is proposed based on the well-known Gutzwiller wave function. We calculate the physical properties using the Monte Carlo algorithm to consider the strong correlation effects. The ground state energy is improved considerably by taking into account electron-hole excitation effects.

Journal of the Physical Society of Japan•Mar 15, 1999•1 citation

Gutzwiller Variational Approximation to the Heavy-Fermion Ground State of the Periodic Anderson Model

Thomas Maurice Rice, Kazuhiro Ueda

A variational wave function for the Kondo-lattice limit of the periodic Anderson model is evaluated with a Gutzwiller approximation. We obtain a characteristic energy from this coherent wave function of the Kondo form but with a different exponent in the case of finite degeneracy. The effective mass and charge and spin susceptibilities are evaluated, and only in the case of large degeneracy and not too small hybridization strength is a heavy-Fermi-liquid state stable against magnetic order.

Physical Review Letters•Aug 26, 1985•304 citations
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.
We propose a new variational wave function for the periodic Anderson model in the case of antiferromagnetically ordered f-electrons. Expectation values in terms of this wave function can be calculated analytically in arbitrary dimensions d. The wave function automatically produces the exact limiting behavior of the ground state energy for weak hybridization and strong f-electron interaction in the symmetric case, which the Gutzwiller wave function fails to do. Several additional improvements are discussed. Thereby one obtains a wave function that leads to extremely good ground state energies for the periodic Anderson model for arbitrary U in all dimensions d.
Abstract We discuss a variational ground state wave function for the symmetric periodic Anderson model with commensurate spin density order. The energy of this ansatz is evaluated in closed form. Our approach generalizes a variational treatment proposed recently by Strack and Vollhardt and results in significantly lower energy. Contrary to the Gutzwiller ansatz the wave function recovers the Schrieffer‐Wolff limit for large Coulomb repulsion. We clarify the relation of our approach to unrestricted Hartree‐Fock and present a comparison with existing quantum Monte Carlo calculations for one dimension.
We investigate Gutzwiller-correlated wave functions as variational ground states for the periodic Anderson model. We extend a recently developed technique for the Hubbard model to the case of two hybridized bands with degeneracy N. We calculate expectation values in the following limits: dilute system (single-impurity case), large degeneracy N, and large dimension d. The mean-field results using the slave-boson approach of Coleman and of Kotliar and Ruckenstein are reproduced in the large-N and large-d limit, respectively. These techniques, therefore, obey variational principles at T=0 in the respective limits and their applicability for T>0 is naturally limited to the Fermi-liquid regime. Evaluations of Gutzwiller-correlated wave functions using the ``Gutzwiller approximation'' are seen to become exact in the limit of large dimensions. A systematic expansion in 1/d can be performed for N=2. In general, corrections are small, of order 1/(dN).
An efficient variational procedure to calculate the ground-state properties of the particle-hole symmetric periodic Anderson model is presented. Expectation values are calculated by using an approximate scheme. It is shown that the ground-state energy calculated with the one-site approximation, which essentially is a single-site mean-field approximation, is identical to the corresponding energy obtained by the well-known Gutzwiller wave function using the Gutzwiller approximation. The two-site approximation, in which intersite correlations are explicitly included, is shown to be a better approximation than the Gutzwiller approximation.