RTGW2020: An efficient implementation of the multi-orbital Gutzwiller method with general local interactions

In the present paper, we propose an efficient numerical scheme for Gutzwiller method for multi-band Hubbard models with general onsite Coulomb interaction. Following the basic idea of Deng et al. (2009) [26] and extensions by Lanata et al. (2012) [28], the ground state is variationally determined through optimizing the total energy with respect to the variational single particle density matrix (n(0)), which is called outer loop. In the corresponding inner loop where n(0) is fixed, the non-interacting wave function and the parameters contained in the Gutzwiller projector are determined by a two-step iterative approach. All derivatives of the implementation process have been analytically derived, which allows us to apply some advanced minimization or root-searching algorithms for both the inner and outer loops leading to the highly efficient convergence. In addition, an atomic diagonalization method taking the point group symmetry into account has been developed for the customized design of the Gutzwiller projector, making it convenient to explore many interesting orders at a lower cost of computation. As benchmarks, several different types of correlated models have been studied utilizing the proposed method, which are in perfect agreement with the previous results by DMFT and multi-orbital slaveboson mean field method. Compared with the linear mixing method, Newton's method with analytical derivatives shows much faster convergence for the inner loop. As for the outer loop, the minimization using analytical derivatives also shows much better stability and efficiency compared with that using numerical derivatives. (C) 2022 Published by Elsevier B.V.

Automated summary

In this paper, an efficient numerical scheme for multi-band Hubbard models using Gutzwiller method is proposed, which optimizes the total energy to variational determine the ground state and develops an atomic diagonalization method. The results show that the method exhibits fast convergence and efficiency in both inner and outer loops, with better stability and efficiency compared to conventional methods.