Gutzwiller method

AB-INITIO GUTZWILLER METHOD FIRST APPLICATION TO PLUTONIUM... 

Among numerous theoretical approaches, the Gutzwiller method [11,12] provides a transparent physical interpretation in term of atomic configurations of a given site. Originally it was applied to the one-band Hubbard model Hamiltonian [13] ... 

Figure 5. Quasiparticles density of states obtained from Gutzwiller method for Plutonium in S phase.

By using the d-wave concept of Kotliar and liu (1988), a conventional (BCS-like) single-band singlet-pair wave function (BCS-hke) wiU be achieved when electron double occupancies are removed by applying the Gutzwiller method (Gutzwiller, 1963). 

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]. 

Moreover, new semiclassical methods have been developed that are based on the Gutzwiller and Berry-Tabor trace formulas [12, 13]. These methods allow the calculation of energy levels or quantum resonances in systems with many interfering periodic orbits, as is the case for chaotic dynamics. 

About 50 years after Einstein, Gutzwiller applied the path integral method with a semiclassical approximation and succeeded to derive an approximate quantization condition for the system that has fully chaotic classical counterpart. His formula expresses the density of states in terms of unstable periodic orbits. It is now called the Gutzwiller trace formula [9,10]. In the last two decades, several physicists tested the Gutzwiiler trace formula for various... 

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. 

In order to exhibit the basic ideas of Gutzwiller s method, we follow an elegant derivation of the trace formula given by Miller (1975). We restrict ourselves to a two degree of freedom bounded autonomous system with Hamiltonian H. The spectrum of H is discrete and determined by... 

Quantized chaos, or quantum chaology (see Section 4.1), is about understanding the quantum spectra and wave functions of classically chaotic systems. The semiclassical method is one of the sharpest tools of quantum chaology. As discussed in Section 4.1.3 the central problem of computing the semiclassical spectrum of a classically chaotic system was solved by Gutzwiller more than 20 years ago. His trace formula (4.1.72) is the basis for all semiclassical work on the quantization of chaotic systems. 

The picture of a low energy, low temperature, Fermi liquid can also be obtained by several projection methods for minimizing the Coulomb interaction energy (Gutzwiller 1965, Coleman 1984, Grewe and Keiter 1981). The first of these methods was developed by Gutzwiller (1965). These methods basically renormalize the hybridization width A by... 

A variety of munerical methods have been used to elucidate the existence of phase separation in the groimd states of the Hubbard and models of the Cu-0 planes of cuprate perovskites. States with charge density waves (CDW), which can be interpreted as stripes, were obtained in Refs. [24-26,29-32] by using the mean-field approximation, the variational principle with the Gutzwiller-type variational fimctions, and the density matrix renormalization group calculations. However, the results of the Monte Carlo simulations [33-35] and cluster calculations [36,37] cast doubt on this finding. Thus, the issue of whether a purely electronic mechanism can explain the stripe formation is still an open question. 

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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