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Efficient implementation of the Gutzwiller variational method

Artikel i vetenskaplig tidskrift
Författare Nicola Lanata
Hugo Strand
Xi Dai
Bo Hellsing
Publicerad i Physical Review B. Condensed Matter and Materials Physics
Volym 85
Nummer/häfte 3
Sidor artikel nr 035133
ISSN 1098-0121
Publiceringsår 2012
Publicerad vid Institutionen för fysik (GU)
Sidor artikel nr 035133
Språk en
Länkar fy.chalmers.se/~hellsing/publicatio...
https://doi.org/10.1103/PhysRevB.85...
Ämnesord Gutzwiller, strong correlation
Ämneskategorier Elektronstruktur

Sammanfattning

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 mini- mization 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 deter- mined 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.

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