A new FHNC scheme for Gutzwiller correlated wave functions

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

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.

Chunhua Li

P. Fazekas

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.

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.

Robert Joynt, Claudius Gros, Thomas Maurice Rice