The Gutzwiller conjugate gradient minimization method for correlated electron systems

Abstract

We review our recent work on the Gutzwiller conjugate gradient minimization method, an ab initio approach developed for correlated electron systems. The complete formalism has been outlined that allows for a systematic understanding of the method, followed by a discussion of benchmark studies of dimers, one- and two-dimensional single-band Hubbard models. In the end, we present some preliminary results of multi-band Hubbard models and large-basis calculations of F2 to illustrate our efforts to further reduce the computational complexity.

Ground and excited states of even-numbered Hubbard ring at half-filling: comparison of the extended Gutzwiller approach with exact diagonalization

“…Mature tools do exist in evaluating variational wavefunctions for large systems, such as the variational Monte Carlo [36][37][38] or an alternative random-sampling method [39,40]. The GCGM method [14,15] represents an even more efficient approach. The central part of these methods is to minimize the Rayleigh quotient [41], which corresponds to the diagonal terms of the matrices in equation (8).…”

“…For example, the quantum Monte Carlo method [7,8], the density matrix renormalization group (DMRG) scheme [9][10][11], the dynamical variational principle [12,13], and the symmetryprojected variational approach [6]. Our previously developed Gutzwiller conjugate gradient minimization (GCGM) theory [14,15] constitutes another efficient approach for describing strongly correlated electron systems, which has proved to provide satisfying accuracy of the ground-state (GS) energy and wavefunction of 1D and 2D Hubbard models [16,17]. GCGM is based on the Gutzwiller wave function (GWF) proposed by Gutzwiller in 1960s [18,19].…”

A rotationally invariant approach based on Gutzwiller wave function for correlated electron systems

“…But the scaling of the approaches can be exponential, as in configuration interaction, or at least a high power, as in several other state-of-the-art quantum chemistry methods, which makes it difficult to study large systems using these approaches. As an ab initio many-body approach that is both affordable and reasonably accurate, we have been developing the Gutzwiller conjugate gradient minimization (GCGM) method [8][9][10][11][12][13] for studying the correlated electron systems. The GCGM method is based on the Gutzwiller variational wave function (GWF) |Ψ GWF ⟩ [14][15][16], which is constructed by applying a correlation operator on a trial noninteracting wavefunction |Ψ 0 ⟩ so that each on-site valence electronic configuration is assigned an adjustable amplitude and phase factor.…”

“…If the two Fluorine atoms are aligned along the z-axis, we may group the 2p x , 2p y orbitals (since the 2p x orbital overlaps with 2p y after rotation by 90 • about the z-axis) and use the number of electrons that occupying either of the p− orbitals to parametrize the system. Some of the results presented in this work has been published preliminarily in [9], but still, the approach and the results deserve a separate publication for completeness of the approach. The scope of this work is restricted to energy calculation of dimers, but the RI approach can be naturally extended to more complex systems such as larger molecules and bulk systems as illustrated in [9].…”

“…Some of the results presented in this work has been published preliminarily in [9], but still, the approach and the results deserve a separate publication for completeness of the approach. The scope of this work is restricted to energy calculation of dimers, but the RI approach can be naturally extended to more complex systems such as larger molecules and bulk systems as illustrated in [9].…”