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

Fermi hypernetted-chain theory for correlated spin-density-wave states

X. Q. G. Wang, Stefano Fantoni, Erio Tosatti, Lianchun Yu

Published Oct 1, 1992• 6 citations
Publisher

Abstract

The Fermi hypernetted-chain (FHNC) theory is applied to spin-density-wave states combined with a Jastrow-type correlation operator. The commonly used approximation scheme FHNC/n is found to be unsuitable for dealing with this class of correlated wave functions. A new scheme, named FHNC-n, is proposed, and numerically tested for the one-dimensional (1D) Hubbard model and the Gutzwiller correlation operator. The results obtained are in very good agreement with the available variational Monte Carlo calculation. This scheme can be used to study 2D and 3D Hubbard models and can easily be extended to treat more general correlation operators, which include triplet and quartet correlations.

DOI
10.1103/physrevb.46.8894

Related papers

Gutzwiller approximation in the Fermi hypernetted-chain theory

Xiao-Qian Wang, C. E. Campbell

We present a general formalism for the variational calculation of the one-body density-matrix and correlation functions for strongly correlated lattice electrons in terms of the Fermi hypernetted-chain (FHNC) diagrammatic expansion. It is shown that, in the limit of infinite spatial dimensions, the local-field-approximate FHNC scheme yields the exact solution for the Gutzwiller wave function, which is equivalent to the result of the Gutzwiller approximation.

Physical review. B, Condensed matter•Jun 15, 1993•1 citation

A new hypernetted-chain treatment for Laughlin quantum Hall states

Orion Ciftja, Stefano Fantoni

The hypernetted-chain theory is applied to study the fractional quantum Hall effect with the Laughlin wave functions. A new method is proposed to include the effect of the elementary diagrams, which improves upon the commonly used modified hypernetted-chain approximation. The correlation energy, the pair distribution function, as well as the magnetoroton excitation spectrum have been computed within this method. The results obtained are in very good agreement with the available Monte Carlo estimates. The method is generalizable to treat other wave functions, like those corresponding to the hierarchical states or those of composite fermion type.

Europhysics Letters (EPL)•Dec 20, 1996•17 citations

Fermi-hypernetted-chain scheme for Gutzwiller correlated wave functions

X. Q. G. Wang, Stefano Fantoni, Erio Tosatti +1 more

A set of integral equations in the Fermi-hypernetted-chain scheme is formulated for Gutzwiller correlated wave functions. The well-known exact analytical results of Vollhardt, Metzner, and Gebhard for the one- and infinite-dimensional Gutzwiller paramagnetic wave functions are recovered as a byproduct of the theory. In approximate form, the theory is applicable to arbitrary Gutzwiller correlated wave functions, irrespective of the space dimensionality of the model.

Physical review. B, Condensed matter•Apr 1, 1994•3 citations

Application of Fermi-hypernetted-chain theory to composite-fermion quantum Hall states

Orion Ciftja, Stefano Fantoni

The Fermi-hypernetted-chain (FHNC) theory and the effective hypernetted-chain method are applied to study the composite-fermion (CF) states of the fractional quantum Hall effect. Using this theory we compute, in the thermodynamic limit, the correlation energy, radial distribution function, and static structure factor for all unprojected CF wave functions. The unprojected excitation gaps for $\ensuremath{\nu}=1/3,1/5$ were obtained by adopting in the FHNC a scheme previously used to compute nuclear matter excitation spectra. The results obtained so far are consistent with Monte Carlo simulations and small-number exact diagonalizations.

Physical review. B, Condensed matter•Nov 15, 1997•26 citations

An analysis of variational wave function for the pairing problem in strongly correlated system

Hsuan‐Hao Fan, E. Krotscheck

We report a theoretical analysis of variational wave functions for the BCS pairing problem. Starting with a Jastrow-Feenberg (or, in a more recent language "fixed-node") wave function for the superfluid state, we develop the full optimized Fermi-Hypernetted Chain (FHNC-EL) equations which sum a local approximation of the parquet-diagrams. Close examination of the procedure reveals that it is essential to go beyond the usual Jastrow-Feenberg approximation to guarantee the correct stability range.

arXiv:1801.10196•Journal of Physics Conference Series•Jun 1, 2018•3 citations

Method of correlated basis functions and FHNC theory

Pavlos M. Hatzikonstantinou, J M Irvine

A method for the accurate evaluation of the diagonal and off-diagonal matrix elements of the Hamiltonian operator within the correlated basis function scheme is presented. Considering a basis consisting of Slater determinants, correlated with a Jastrow correlation factor, the expectation value of the kinetic energy operator has been expressed in the Jackson-Feenberg form. A diagrammatic analysis is presented for the construction and evaluation of the cluster expansions of the required quantities incorporating the Fermi hypernetted chain theory.

Journal of Physics A Mathematical and General•May 1, 1982•2 citations
The Fermi hypernetted-chain (FHNC) theory is applied to spin-density-wave states combined with a Jastrow-type correlation operator. The commonly used approximation scheme FHNC/n is found to be unsuitable for dealing with this class of correlated wave functions. A new scheme, named FHNC-n, is proposed, and numerically tested for the one-dimensional (1D) Hubbard model and the Gutzwiller correlation operator. The results obtained are in very good agreement with the available variational Monte Carlo calculation. This scheme can be used to study 2D and 3D Hubbard models and can easily be extended to treat more general correlation operators, which include triplet and quartet correlations.
The hypernetted-chain theory is applied to study the fractional quantum Hall effect with the Laughlin wave functions. A new method is proposed to include the effect of the elementary diagrams, which improves upon the commonly used modified hypernetted-chain approximation. The correlation energy, the pair distribution function, as well as the magnetoroton excitation spectrum have been computed within this method. The results obtained are in very good agreement with the available Monte Carlo estimates. The method is generalizable to treat other wave functions, like those corresponding to the hierarchical states or those of composite fermion type.
The Fermi-hypernetted-chain (FHNC) theory and the effective hypernetted-chain method are applied to study the composite-fermion (CF) states of the fractional quantum Hall effect. Using this theory we compute, in the thermodynamic limit, the correlation energy, radial distribution function, and static structure factor for all unprojected CF wave functions. The unprojected excitation gaps for $\ensuremath{\nu}=1/3,1/5$ were obtained by adopting in the FHNC a scheme previously used to compute nuclear matter excitation spectra. The results obtained so far are consistent with Monte Carlo simulations and small-number exact diagonalizations.
We report a theoretical analysis of variational wave functions for the BCS pairing problem. Starting with a Jastrow-Feenberg (or, in a more recent language "fixed-node") wave function for the superfluid state, we develop the full optimized Fermi-Hypernetted Chain (FHNC-EL) equations which sum a local approximation of the parquet-diagrams. Close examination of the procedure reveals that it is essential to go beyond the usual Jastrow-Feenberg approximation to guarantee the correct stability range.
A method for the accurate evaluation of the diagonal and off-diagonal matrix elements of the Hamiltonian operator within the correlated basis function scheme is presented. Considering a basis consisting of Slater determinants, correlated with a Jastrow correlation factor, the expectation value of the kinetic energy operator has been expressed in the Jackson-Feenberg form. A diagrammatic analysis is presented for the construction and evaluation of the cluster expansions of the required quantities incorporating the Fermi hypernetted chain theory.