Comparison of variational wavefunctions for correlated systems

Balázs Hetényi

Franjo Franjic

C. Stephen Hellberg, E. J. Melé

We study a general class of variational wavefunctions for strongly correlated lattice fermions. The wavefunctions considered here automatically satisfy local constraints of no double occupancy and include correlations between opposite spin particles in a very physical way. We calculate the energy and correlation functions for the one dimensional U=∞ Hubbard model, where a comparison with exact results is made. We briefly report on preliminary results for the t-J model.

Jeffrey Ting Fung Poon

In this thesis, we present theoretical analysis of Fermi liquid theory for Hubbard model on a triangular lattice. In particular, the wavefunction and Landau parameters for the system are calculated and analyzed. We start with calculations of the wavefunction and Landau parameters in perturbation theory, both numerically and analytically (for some special cases). The calculation will then be promoted to a variation calculation by modifying the coefficients in the perturbed wavefunction in the perturbation theory. Numerical results for the wavefunction and Landau parameters will be presented. Comparisons between perturbation and variation calculations will be carried out in different scenario, for example, different spatial direction so as to predict the general features of variation refinement of the problem given above.

Brett A. Cagg, Vitaly A. Rassolov

Strong orthogonality is an important constraint placed on geminal wavefunctions in order to make variational minimization tractable. However, strong orthogonality prevents certain, possibly important, excited configurations from contributing to the ground state description of chemical systems. The presented method lifts strong orthogonality constraint from geminal wavefunction by computing a perturbative-like correction to each geminal independently from the corrections to all other geminals. The method is applied to the Singlet-type Strongly orthogonal Geminals variant of the geminal wavefunction. Comparisons of this new SS(p)G method are made to the non-orthogonal AP1roG and the unconstrained Geminal Mean-Field Configuration Interaction method using small atomic and molecular systems. The correction is also compared to Density Matrix Renormalization Group calculations performed on long polyene chains in order to assess its scalability and applicability to large strongly correlated systems. The results of these comparisons demonstrate that although the perturbative correction is small, it may be a necessary first step in the systematic improvement of any strongly orthogonal geminal method.