Efficient implementation of the Gutzwiller variational method

Abstract

We present a self-consistent numerical approach to solve the Gutzwiller variational problem for general multi-band models with arbitrary on-site interaction. The proposed method generalizes and improves the procedure derived by Deng et al., Phys. Rev. B. 79 075114 (2009), overcoming the restriction to density-density interaction without increasing the complexity of the computational algorithm. Our approach drastically reduces the problem of the high-dimensional Gutzwiller minimization by mapping it to a minimization only in the variational density matrix, in the spirit of the Levy and Lieb formulation of DFT. For fixed density the Gutzwiller renormalization matrix is determined as a fixpoint of a proper functional, whose evaluation only requires ground-state calculations of matrices defined in the Gutzwiller variational space. Furthermore, the proposed method is able to account for the symmetries of the variational function in a controlled way, reducing the number of variational parameters. After a detailed description of the method we present calculations for multi-band Hubbard models with full (rotationally invariant) Hund's rule on-site interaction. Our analysis shows that the numerical algorithm is very efficient, stable and easy to implement. For these reasons this method is particularly suitable for first principle studies -- e.g., in combination with DFT -- of many complex real materials, where the full intra-atomic interaction is important to obtain correct results.Comment: 19 pages, 7 figure

γ−αIsostructural Transition in Cerium

“…al], which further improves the method previously proposed in Ref. [3], and is a generalization of earlier formulations of the GA [4][5][6][7][8].…”

“…4, can be interpreted as a consequence of the above-mentioned reduction of effective f -level degeneracy -a well known effect in the theory of the single-ion Kondo impurity. As in the early Kondo volume collapse theory [3], ∂Z/∂V contributes to the pressure. However, some qualitative features of our solution, such as the form of the pressure-volume phase diagram, show that other physical elements, such as the changes in the charge density induced by the correlations, have to also be included in realistic theories of this material.…”

“…Furthermore, the possibility that the underlying mechanism lies in the electronic structure only -i.e., without it being necessary to involve other effects -makes Cerium a potential theoretical testing ground for basic concepts of correlated electron systems. Two main theoretical pictures are still under debate to explain the volume collapse: the Kondo volume collapse (KVC) [3,4] and the orbital-selective Mott transition within the Hubbard model (HM) [5]. According to the KVC the transition is induced by the rapid change of the coherence temperature across the transition boundaries, which affect dramatically the structure of the conduction spd electrons through Kondo effect.…”

“…Another key requirement is that the two phases are treated within the same theoretical framework. In this work, we use a combination of Density Functional Theory and the Gutzwiller Approximation (LDA+GA) [19][20][21][22][23] [24], which removes many of the approximations inherent in previous studies. As a benchmark, in the supplementary material we present also LDA+DMFT calculations for Cerium.…”

Phase Diagram and Electronic Structure of Praseodymium and Plutonium

“…[20]. The GA approximation was, thereafter, extensively developed [21][22][23][24][25][26][27], and it has been formulated and implemented in combination with realistic electronic structure calculations such as the LDA þ GA approach [23,28], which has been applied successfully to many systems [29][30][31][32][33][34][35][36]. A third important many-body technique is the slave boson approach (SB) [37,38], which is, in principle, an exact reformulation of the quantum many-body problem for model Hamiltonians, and it reproduces the results of the GA at the saddle-point level [24,39].…”