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.

19 pages, 7 figures

References in corpus (10)

• Spin freezing transition and non-Fermi-liquid self-energy in a 3-orbital model
• High-spin to low-spin and orbital polarization transitions in multiorbital Mott systems
• Time-Dependent Mean Field Theory for Quench Dynamics in correlated electron systems
• Rotationally-invariant slave-boson formalism and momentum dependence of the quasiparticle weight
• Metal-Insulator phase diagram and orbital selectivity in 3-orbital models with rotationally invariant Hund coupling
• Dynamical behavior across the Mott transition of two bands with different bandwidths
• Gutzwiller density functional theory for correlated electron systems
• Equivalence of Gutzwiller and slave-boson mean-field theories for multi-band Hubbard models
• Gutzwiller description of non-magnetic Mott insulators: a dimer lattice model
• Convergence acceleration and stabilization for dynamical-mean-field-theory calculations

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