LDA+Gutzwiller Method And It’s Application In Strongly Correlated Electronic Systems

The formal inception and successful development of density functional theory since 1960s makes large scale ab initio calculations for realistic materials gain widespread popularity and blossom in various academic and engineering branches.The first principle method based on Kohn-Sham equation,however,always fails in the strongly correlated materials where 3d or 4-5f orbital electrons dominate.The LDA+Gutzwiller method developed in our group can not only obtain the ground state of the strongly correlated materials very fast but also be as accurate as the dynamic mean field theory,while the current implementation always has difficulty in convergence for many complex materials.In this PHD thesis,I try to employ new variational framework,analytical derivatives as well as heterogeneous architecture to generally improve the convergence and computational efficiency of the LDA+Gutzwiller method.Whereafter,we have studied the electronic structures of normal state and possible order parameters of hidden order state of the celebrated heavy Fermion materials URu2Si2 with the newly developed method.The LDA+Gutzwiller method is a non-perturbative many-body numerical method which adopts the Gutzwiller wave function Ansatz to approximately solve the generalized multi-orbital Hubbard models from first principles.How to obtain the ground state efficiently is the key part of the concrete implementation.The traditional approach converts the equation set of the first order derivatives of the total energy functional with respect to the non-interacting wave function as well as the Gutzwiller variational parameters to a two-variable self-consistent problem through linear search method.But it’s hard for the two variables to achieve convergence simultaneously in the implementation of the self-consistent problem.Now,we utilize new variational scheme to transfer the two-variable self-consistent process to two nested loops.The outer loop is a constrained minimization problem of variational single-particle density matrix while the inner loop is a self-consistent process of orbital renormalization factors.That has greatly improved the low speed and instability of the convergence iterations.Meanwhile,we realized new algorithm for the atomic problem,which enables us to customize the Gutzwiller variational parameters with respect to the point group very conveniently.Based on the proposed algorithm,we have developed a first principle electronic structure software for strongly correlated materials,dubbed as RTGW2020,which has various advantages,like fast and stable convergence,supporting for heterogeneous parallelism and automatic scripts for pre-/post-process.Benchmarks on various standard Hubbard models and calculations for realistic materials have proven the accuracy and efficiency as well as stability of this method.Finally,we studied the normal state of the celebrated heavy Fermion material URu2Si2 by the newly developed LDA+Gutzwiller method.Based on the local manybody density matrix,we made some reasonable predictions for the order parameter of the hidden order.To make the calculation as accurate as possible,we include kinetic term,Coulomb interaction,crystal field as well as spin-orbital coupling in the model Hamiltonian.Besides,with the help of newly developed atom subroutine,we considered all the symmetry allowed Gutzwiller variational parameters which amounts to 1921 in total in the Gutzwiller trial wave function.The results show three main features.Firstly,the band width of the quasiparticle has been suppressed heavily with the quasiparticle weight between 0.2 and 0.5.Besides,the weight decreases with the increase of the correlated electron occupancy.Secondly,the off-diagonal Gutzwiller variational parameters are about one or two orders of magnitude smaller than the diagonal parameters,indicating the off-diagonal parameters are thus not significant to the normal state of URu2Si2.Finally,the first two predominant eigenstates of the many-body density matrix belong to Alg and A2g irreducible representation of the double point group D4h,which suggests the hexadecapole(Hzα)to be the most promising candidate of the hidden order.Besides,several other excited eigenstates also have non-negligible probabilities,leading to the possible emergence of quadrupole(?22,?xy)and octupole(Txyz,Tzβ).