Ground state wave functions for single-band Hubbard models from the Gutzwiller conjugate gradient minimisation theory

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

It remains a great challenge in condensed matter physics to develop a method to treat strongly correlated many-body systems with balanced accuracy and efficiency. We introduce an extended Gutzwiller (EG) method incorporating a manifold technique, which builds an effective manifold of the many-body Hilbert space, to describe the ground-state (GS) and excited-state (ES) properties of strongly correlated electrons. We systematically apply an EG projector onto the GS and ES of a non-interacting system. Diagonalization of the true Hamiltonian within the manifold formed by the resulting EG wavefunctions gives the approximate GS and ES of the correlated system. To validate this technique, we implement it on even-numbered fermionic Hubbard rings at half-filling with periodic boundary conditions, and compare the results with the exact diagonalization (ED) method. The EG method is capable of generating high-quality GS and low-lying ES wavefunctions, as evidenced by the high overlaps of wavefunctions between the EG and ED methods. Favorable comparisons are also achieved for other quantities including the total energy, the double occupancy, the total spin and the staggered magnetization. With the capability of accessing the ESs, the EG method can capture the essential features of the one-electron removal spectral function that contains contributions from states deep in the excited spectrum. Finally, we provide an outlook on the application of this method on large extended systems.

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

We introduce a rotationally invariant approach combined with the Gutzwiller conjugate gradient minimization method to study correlated electron systems. In the approach, the Gutzwiller projector is parametrized based on the number of electrons occupying the onsite orbitals instead of the onsite configurations. The approach efficiently groups the onsite orbitals according to their symmetry and greatly reduces the computational complexity, which yields a speedup of20∼50×in the minimal basis energy calculation of dimers. The computationally efficient approach promotes more accurate calculations beyond the minimal basis that is inapplicable in the original approach. A large-basis energy calculation of F₂demonstrates favorable agreements with standard quantum-chemical calculations Bytautaset al(2007J. Chem. Phys.127164317).

The Gutzwiller conjugate gradient minimization method for correlated electron systems

We review our recent work on the Gutzwiller conjugate gradient minimization method, anab initioapproach 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 F₂to illustrate our efforts to further reduce the computational complexity.