Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries and characterizations of strongly correlated electron materials and by requirements for understanding mechanisms of intriguing phenomena beyond a single-particle picture. A three-stage scheme is developed as renormalized multi-scale solvers (RMS) utilizing the hierarchical electronic structure in the energy space. It provides us with an ab initio downfolding of the global band structure into low-energy effective models followed by low-energy solvers for the models. The RMS method is illustrated with examples of several materials. In particular, we overview cases such as dynamics of semiconductors, transition metals and its compounds including iron-based superconductors and perovskite oxides, as well as organic conductors of kappa-ET type.
Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries and characterizations of strongly correlated electron materials and by requirements for understanding mechanisms of intriguing phenomena beyond a single-particle picture. A three-stage scheme is developed as renormalized multi-scale solvers (RMS) utilizing the hierarchical electronic structure in the energy space. It provides us with an ab initio downfolding of the global band structure into low-energy effective models followed by low-energy solvers for the models. The RMS method is illustrated with examples of several materials. In particular, we overview cases such as dynamics of semiconductors, transition metals and its compounds including iron-based superconductors and perovskite oxides, as well as organic conductors of kappa-ET type.
Substantial progress has been achieved in the last couple of decades in computing the electronic structure of correlated materials from first principles. This progress has been driven by parallel development in theory and numerical algorithms. Theoretical development in combining ab initio approaches and many-body methods is particularly promising. A crucial role is also played by a systematic method for deriving a low-energy model, which bridges the gap between real and model systems. In this article, an overview is given tracing the development from the LDA+U to the latest progress in combining the G W method and (extended) dynamical mean-field theory ( G W +EDMFT). The emphasis is on conceptual and theoretical aspects rather than technical ones.
The discovery of high-Tc superconductivity in cuprates in 1986 moved strongly correlated systems from exotic worlds interesting only for pure theorists to the focus of solid-state research. In recent decades, the majority of hot topics in condensed matter physics (high-Tc superconductivity, colossal magnetoresistance, multiferroicity, ferromagnetism in diluted magnetic semiconductors, etc.) have been related to strongly correlated transition metal compounds. The highly successful electronic structure calculations based on density functional theory lose their predictive power when applied to such compounds. It is necessary to go beyond the mean field approximation and use the many-body theory. The methods and models that were developed for the description of strongly correlated systems are reviewed together with the examples of response function calculations that are needed for the interpretation of experimental information (inelastic neutron scattering, optical conductivity, resonant inelastic X-ray scattering, electron energy loss spectroscopy, angle-resolved photoemission, electron spin resonance, and magnetic and magnetoelectric properties). The peculiarities of (quasi-) 0-, 1-, 2-, and 3- dimensional systems are discussed.
Computational chemistry has made remarkable progress in the last couple of decades due to the availability of better and more powerful computers. However, there is definitely more room for improvement. There are problems in material science and biology that require 102 to 104 atoms to be considered and the importance of such systems cannot be over-emphasized. Addressing such systems with ab-initio methods is still a quantum chemist’s dream. ¨ Brute force solutions of the Schrodinger equation are not possible for reasonably interesting and important systems due to the large number of Slater determinants that have to be stored in a computer’s memory. Thus electronic structure theorists have made chemically and mathematically intuitive approximations to simplify the problems. A particularly difficult class of systems that is very interesting to the theoretical and experimental chemists is the strongly correlated systems. High Tc superconductors, nanotubes, graphene sheets, transition metal complexes and photosynthetic materials all fall under this category. These systems are too large to be treated by traditional quantum chemical methods. Another reason why such systems have not been studied sufficiently by ab-initio method is that they comprise of complicated strong electron-electron correlation (and therefore the name strongly correlated), thus, making them impossible to be qualitatively defined by a molecular orbital picture, which has been a quantum chemist’s fa- vorite tool for a long time now. Therefore, in this thesis, we have tried to develop, improve and apply methods for treating such strongly correlated systems. The thesis is broadly divided into two parts. In the first part, we discuss the orbital optimized DMRG method developed to treat static correlation in large strongly correlated systems. In the next part we discuss the two methods that can treat dynamic correlation in such complicated systems.
We propose a new, alternative method for ab-initio calculations of the electronic structure of solids, which has been specifically adapted to treat many-body effects in a more rigorous way than many existing ab-initio methods. We start from a standard band-structure calculation for an effective one-particle Hamiltonian approximately describing the material of interest. This yields a suitable set of one-particle basis functions, from which well localized Wannier functions can be constructed using a method proposed by Marzari and Vanderbilt. Within this (minimal) basis of localized Wannier functions the matrix elements of the non-interacting (one-particle) Hamiltonian as well as the Coulomb matrix elements can be calculated. The result is a many-body Hamiltonian in second quantization with parameters determined from first principles calculations for the material of interest. The Hamiltonian is in the form of a multi-band Hamiltonian in second quantization (a kind of extended, multi-band Hubbard model) such that all the standard many-body methods can be applied. We explicitly show how this approach can be solved in the simplest many-body approximation, the mean-field Hartree-Fock approximation (HFA), which takes into account exact exchange and corrects for self-interaction effects.
A variety of quantum many-body methods have been developed for studying the strongly correlated electron systems. We have also proposed a computationally efficient and accurate approach, named the correlation matrix renormalization (CMR) method to address the challenges. The theoretic development and benchmark tests of the CMR method are included in this thesis. Meanwhile, ground state total energy is the most important property of electronic calculations. We also investigated an alternative approach to calculate the total energy, and extended this method for magnetic anisotropy energy of ferromagnetic materials. In addition, another theoretical tool, dynamical mean-field theory on top of the density functional theory, has also been used in electronic structure calculations for an Iridium oxide to study the phase transition, which results from an interplay of the d electrons' internal degrees of freedom.
Achieving materials-specific predictions for large, realistic molecules and solids with strong electron correlations remains a long-standing challenge in quantum chemistry. This dissertation develops scalable ab initio quantum many-body methods for crystalline materials, demonstrating that rigorous optimization of theoretical approximations and numerical algorithms enables predictive computation even in strongly correlated systems. The work tackles three interconnected challenges, namely describing material-specific properties of strongly correlated superconductors, achieving linear scaling with k-points for large-scale periodic calculations, and establishing reliable methods for electron-phonon interactions. The following chapters address each challenge in turn. Chapter 2 demonstrates that ab initio density matrix embedding theory, combined with symmetry-breaking strategies for superconducting order parameters, reproduces experimental trends in cuprate superconductivity, including pressure and layer effects on transition temperatures. By directly solving the electronic Schrödinger equation from material structures, these calculations capture multi-orbital covalency effects that simplified model Hamiltonians neglect, revealing their essential role in the spin fluctuations driving pairing. This predictive capability establishes a foundation for efficient computational screening of superconducting materials. Extending these calculations to larger k-point meshes and broader phase diagram explorations, however, demands more efficient computational algorithms. To overcome this computational bottleneck, Chapter 3 introduces interpolative separable density fitting framework. This development enables thermodynamic limit calculations with up to 1000 k-points, as validated on diamond, carbon dioxide, nickel monoxide, and cuprate systems. Integration with density matrix embedding theory and local natural orbital methods further yields converged ground-state energies from accurate correlated wavefunction methods such as CCSD(T) for crystalline materials in the thermodynamic limit. With computational efficiency established, the remaining challenge lies in extending the theoretical framework beyond purely electronic degrees of freedom. Chapter 4 addresses this need by establishing exponential ansatz wavefunctions as competitive approaches for electron-phonon systems. Unlike previous treatments based on perturbation theory, systematic benchmarking of coupled cluster theory and variational Lang-Firsov methods on the Holstein model demonstrates, for the first time, that these approaches accurately describe polaron formation across coupling regimes when combined with appropriate reference state optimization. These results provide a foundation for incorporating phonon effects into ab initio studies of superconducting materials. In addition to these methodological advances, GPU acceleration and MPI parallelization enhance computational throughput, enabling efficient large-scale calculations. Together, these developments constitute a computational framework for predictive ab initio quantum many-body calculations in crystalline materials, opening new avenues for understanding and designing strongly correlated quantum materials.