Gutzwiller ground state

In the absence of the interaction U, the ground state is that of uncorrelated electrons j o) and has the form of a Slater determinant. As U is turned on, the weight of doubly occupied sites must be reduced because they cost an additional energy U per site. Accordingly, the trial Gutzwiller wave function (GWF) I/g) is built from the Hartree-like uncorraleted wave function (HWF) l/o),... 

This ab-initio Gutzwiller approach is able to handle correctly the correlation aspects without loosing the ab-initio adjustable parameters free aspect of the more familiar DFT-LDA, and that way, corrects the deficiency of this method. It gives similar results to the methods that account for many-body effects like the LDA+DMFT of Ref. [10] from the ab-initio levels or that can have an orbital dependent potential like in the LDA+ 7 calculation of Ref. [36], which is impossible to DFT-LDA approach. On another hand, we stress again that our approach is clearly variational, and is able to provide an approximate ground state in contrast with those of Refs. [10] and [36]. 

Quantum calculations for a classically chaotic system are extremely hard to perform. If more than just the ground state and a few excited states are required, semiclassical methods may be employed. But it was not before the work of Gutzwiller about two decades ago that a semiclassical quantization scheme became available that is powerful enough to deal with chaos. Gutzwiller s central result is the trace formula which is derived in Section 4.1.3. 

While the Hubbard model can be derived from the Hamiltonian in eqn.(2), the model was invented in an entirely different context, independently by Kanamori [19], Gutzwiller [20] and Hubbard [21]. It was first introduced to explain ferromagnetism in metals. While the simple Hubbard model is now known not to have a ferromagnetic ground state (except in some pathological cases [22]), it has become one of the most widely studied models in the context of metal-insulator transitions [23, 24]. 

In the calculation of electronic structures, the presence of correlations thus always represents a difficulty. Perturbation expansions can account for the two extreme cases the delocalized limit in which the effective repulsion U is low compared to the band width, and the quasi-atomic limit where the electron delocalization modifies only slightly the correlated ground state (Anderson, 1959). Some variational techniques (Hubbard, 1964 Gutzwiller, 1965) allow a treatment of systems with U of the order of jS, but they are difficult to use. New methods have recently been developed for adding a part of the Hubbard Hamiltonian to the LDA (local density approximation) ground state (Czyzyk and Sawatzky, 1994). 

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