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

arXiv:1010.5055 · Physical Review B

Tunneling matrix elements with antiferromagnetic Gutzwiller wave functions

Andrea Di Ciolo, Luca F. Tocchio, Claudius Gros

Published Apr 15, 2011• 0 citations
arXivHTMLPDF

Abstract

We use a generalized Gutzwiller approximation elaborated to evaluate matrix elements with partially projected wave functions and formerly applied to homogeneous systems [N. Fukushima et al., Phys. Rev. B 72, 144505 (2005); B. Edegger et al., Adv. Phys. 56, 927 (2007)]. In the present paper we consider projected single-particle (hole) excitations for electronic systems with antiferromagnetic order and obtain the corresponding tunneling probabilities. The accuracy and the reliability of our analytical approximation is tested using the variational Monte Carlo method. Possible comparisons with experimental results are also discussed.

DOI
10.1103/physrevb.83.165116

Related papers

Evaluation of matrix elements in partially projected wave functions

Noboru Fukushima, Bernhard Edegger, V. N. Muthukumar +1 more

We generalize the Gutzwiller approximation scheme to the calculation of nontrivial matrix elements between the ground state and excited states. In our scheme, the normalization of the Gutzwiller wave function relative to a partially projected wave function with a single nonprojected site (the reservoir site) plays a key role. For the Gutzwiller projected Fermi sea, we evaluate the relative normalization both analytically and by variational Monte Carlo (VMC). We also report VMC results for projected superconducting states that show novel oscillations in the hole density near the reservoir site.

arXiv:cond-mat/0503143•Physical Review B•Oct 7, 2005•13 citations

Novel stochastic approach for Gutzwiller matrix elements: Two-dimensional Hubbard model

P. G. McQueen, C. S. Wang

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.

Physical review. B, Condensed matter•Jun 1, 1989•6 citations

Variational Monte Carlo evaluations of Gutzwiller states for the Anderson-lattice model

P. G. McQueen, C. S. Wang

The electronic ground states for two- and three-dimensional Anderson-lattice clusters with large Hubbard repulsion are determined variationally within the Gutzwiller ansatz by use of a stochastic algorithm for exact evaluation of matrix elements of Gutzwiller states. The algorithm is similar to one normally used for finite-temperature simulation and is described in some detail. Variational states for a variety of Hamiltonian parameters and particle densities were considered. Of particular interest is the regime of small interband hopping, which is antiferromagnetic at densities near two particles per unit cell. We found that for some Hamiltonian-parameter regimes, doping the antiferromagnetic cluster with enough particles or holes can destroy the magnetic ordering and produce a state that resembles a heavy-Fermi-liquid state, a metal with a strongly-frequency-dependent self-energy. For a 4\ifmmode\times\else\texttimes\fi{}4 Anderson lattice, we present results of low-temperature quantum Monte Carlo simulations to evaluate the validity of the variational Gutzwiller ansatz.

Physical review. B, Condensed matter•Nov 1, 1991•6 citations

Self-consistent projection operator approach to excitation spectra: Role of correlated wave function

Y. Kakehashi, Peter Fulde

A recently proposed combination of a projection operator method with the coherent potential approximation for the computation of the excitation spectra of solids is further extended. In particular, the effect of electron correlations on the matrix elements of the self-energy are investigated. This is done with the help of a Gutzwiller-type variational wave function. Numerical calculations have been performed for a half-filled band of a hypercubic lattice in infinite dimensions. They show that for strong electron correlations the higher-order dynamical corrections in an renormalized perturbation expansion are screened except in the low-energy regime. This provides for a justification of earlier work, where a Hartree-Fock approximation with a cutoff parameter was used for the computation of the static matrix elements.

Physical Review B•Oct 27, 2004•3 citations

A new expansion for generalized Gutzwiller wave functions: Antiferromagnetic case

Yuge Li, N. d’Ambrumenil

We propose an alternative approach to the 1/D-type expansions for evaluating properties of generalized Gutzwiller wave functions (GWF’s) in low dimensions. Our expansion uses the sum rule and symmetries of the trial wave function explicitly. We apply the scheme to an antiferromagnetic generalization of the GWF for the 1D Hubbard model. We find good agreement with known results from variational Monte Carlo calculations and a significant improvement over previous approximations.

Journal of Applied Physics•May 15, 1993•3 citations

Order and excitation in partially Gutzwiller projectedt–t′–t″–J–Umodels

Khee-Kyun Voo

Extended t-t'-t"-J-U models in which the second-nearest-neighbor hopping (t') and third-nearest-neighbor hopping (t") are included are studied using renormalized mean field theory. The models are meant to be low-energy effective models for the Hubbard models, and hence the Heisenberg exchange integral J and Hubbard repulsion U are related by J = 4t(2)/U. The trial wavefunctions for the ground states are partially Gutzwiller projected Hartree-Fock states. The Gutzwiller projection is implemented by means of a Gutzwiller approximation, and the site double occupancy d is taken as a variational parameter. It is found that a large |t'/t| narrows the band filling range that sustains antiferromagnetism (AFM) in the ground state, enhances the d-wave singlet superconductivity (dSC) in hole overdoped systems, but suppresses the dSC in electron overdoped systems. For a system that has large |t'/t| and |t"/t'|, the superconductivity (SC) at the onset of AFM in hole doped band filling is strongly suppressed. On the excitation occurring, when an electron doped system simultaneously contains SC and AFM, the system is found to have a nodeless gap at the Fermi level. Finally, the result of this study is related to experiments on the superconducting cuprates.

Journal of Physics Condensed Matter•Nov 18, 2011•5 citations
We use a generalized Gutzwiller approximation elaborated to evaluate matrix elements with partially projected wave functions and formerly applied to homogeneous systems [N. Fukushima et al., Phys. Rev. B 72, 144505 (2005); B. Edegger et al., Adv. Phys. 56, 927 (2007)]. In the present paper we consider projected single-particle (hole) excitations for electronic systems with antiferromagnetic order and obtain the corresponding tunneling probabilities. The accuracy and the reliability of our analytical approximation is tested using the variational Monte Carlo method. Possible comparisons with experimental results are also discussed.
We generalize the Gutzwiller approximation scheme to the calculation of nontrivial matrix elements between the ground state and excited states. In our scheme, the normalization of the Gutzwiller wave function relative to a partially projected wave function with a single nonprojected site (the reservoir site) plays a key role. For the Gutzwiller projected Fermi sea, we evaluate the relative normalization both analytically and by variational Monte Carlo (VMC). We also report VMC results for projected superconducting states that show novel oscillations in the hole density near the reservoir site.
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.
The electronic ground states for two- and three-dimensional Anderson-lattice clusters with large Hubbard repulsion are determined variationally within the Gutzwiller ansatz by use of a stochastic algorithm for exact evaluation of matrix elements of Gutzwiller states. The algorithm is similar to one normally used for finite-temperature simulation and is described in some detail. Variational states for a variety of Hamiltonian parameters and particle densities were considered. Of particular interest is the regime of small interband hopping, which is antiferromagnetic at densities near two particles per unit cell. We found that for some Hamiltonian-parameter regimes, doping the antiferromagnetic cluster with enough particles or holes can destroy the magnetic ordering and produce a state that resembles a heavy-Fermi-liquid state, a metal with a strongly-frequency-dependent self-energy. For a 4\ifmmode\times\else\texttimes\fi{}4 Anderson lattice, we present results of low-temperature quantum Monte Carlo simulations to evaluate the validity of the variational Gutzwiller ansatz.
A recently proposed combination of a projection operator method with the coherent potential approximation for the computation of the excitation spectra of solids is further extended. In particular, the effect of electron correlations on the matrix elements of the self-energy are investigated. This is done with the help of a Gutzwiller-type variational wave function. Numerical calculations have been performed for a half-filled band of a hypercubic lattice in infinite dimensions. They show that for strong electron correlations the higher-order dynamical corrections in an renormalized perturbation expansion are screened except in the low-energy regime. This provides for a justification of earlier work, where a Hartree-Fock approximation with a cutoff parameter was used for the computation of the static matrix elements.
Extended t-t'-t"-J-U models in which the second-nearest-neighbor hopping (t') and third-nearest-neighbor hopping (t") are included are studied using renormalized mean field theory. The models are meant to be low-energy effective models for the Hubbard models, and hence the Heisenberg exchange integral J and Hubbard repulsion U are related by J = 4t(2)/U. The trial wavefunctions for the ground states are partially Gutzwiller projected Hartree-Fock states. The Gutzwiller projection is implemented by means of a Gutzwiller approximation, and the site double occupancy d is taken as a variational parameter. It is found that a large |t'/t| narrows the band filling range that sustains antiferromagnetism (AFM) in the ground state, enhances the d-wave singlet superconductivity (dSC) in hole overdoped systems, but suppresses the dSC in electron overdoped systems. For a system that has large |t'/t| and |t"/t'|, the superconductivity (SC) at the onset of AFM in hole doped band filling is strongly suppressed. On the excitation occurring, when an electron doped system simultaneously contains SC and AFM, the system is found to have a nodeless gap at the Fermi level. Finally, the result of this study is related to experiments on the superconducting cuprates.