Efficient implementation of the Gutzwiller variational method
Efficient implementation of the Gutzwiller variational method
复制标题
DOI：
10.1103/physrevb.85.035133
复制
发表时间：
2012-01-31
影响因子：
3.7
通讯作者：
Hellsing, Bo
中科院分区：
文献类型：
--
作者：
Lanata, Nicola;Strand, Hugo U. R.;Hellsing, Bo
本文提出了一种自洽的数值方法来求解具有任意在位相互作用的一般多带模型的Gutzwiller变分问题。所提出的方法推广和改进了Deng等人[Phys. Rev. B 79，075114（2009）]导出的过程，克服了对密度-密度相互作用的限制，而不增加计算算法的复杂性。我们的方法大大减少了高维Gutzwiller最小化的问题，映射到一个最小化，只有在变分密度矩阵，在密度泛函理论（DFT）的Levy和Lieb制定的精神。对于固定密度的Gutzwiller重整化矩阵被确定为一个适当的功能，其评价只需要基态计算的Gutzwiller变分空间中定义的矩阵的不动点。此外，所提出的方法是能够占的变分函数的对称性在一个控制的方式，减少变分参数的数量。在详细描述的方法，我们提出了计算多带哈伯德模型与完整的（旋转不变）洪德规则现场相互作用。我们的分析表明，数值算法是非常有效的，稳定的，易于实现。由于这些原因，这种方法特别适合于第一性原理研究（e。例如，在一个实施例中，与DFT结合），其中完整的原子内相互作用对于获得正确的结果很重要。
We present a self-consistent numerical approach to solve the Gutzwiller variational problem for general multiband 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 density functional theory (DFT). For fixed density the Gutzwiller renormalization matrix is determined as a fixpoint of a proper functional, whose evaluation requires only 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 multiband 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-principles studies (e. g., in combination with DFT) of many complex real materials, where the full intra-atomic interaction is important to obtain correct results.