1/n expansion and wave functions

Boris Mikhailovich Karnakov, V. D. Mur, В. С. Попов

V. D. Mur, Sergey Georgievich Pozdnyakov, В. С. Попов

Y. M. Li, N. d’Ambrumenil

A systematic expansion scheme that goes beyond the Gutzwiller-type approximation is developed for generalized Gutzwiller wave functions. The expansion satisfies sum rules and symmetries of the trial wave function in a self-consistent way. We apply the scheme to an antiferromagnetic generalization of the Gutzwiller wave function for the one-dimensional Hubbard model. We find good agreement with known results from variational Monte Carlo calculations. We also demonstrate that the expansion scheme converges rapidly.

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.

Robert B. Griffiths

Chen, Changye

In this letter we investigate the common procedure in which any wave function is expanded into a series of eigenfunctions. It is shown that as far as dynamical systems are concerned the expanding procedure involves various mathematical and physical difficulties. With or without introducing phase factors, such expansions do not represent dynamical wave functions.