The quantitative description of correlated electron materials remains a modern computational challenge. We demonstrate a numerical strategy to simulate correlated materials at the fully ab initio level beyond the solution of effective low-energy models and apply it to gain a detailed microscopic understanding across a family of cuprate superconducting materials in their parent undoped states. We uncover microscopic trends in the electron correlations and reveal the link between the material composition and magnetic energy scales through a many-body picture of excitation processes involving the buffer layers. Our work illustrates a path toward a quantitative and reliable understanding of more complex states of correlated materials at the ab initio many-body level.
The quantitative description of correlated electron materials remains a modern computational challenge. We demonstrate a numerical strategy to simulate correlated materials at the fully ab initio level beyond the solution of effective low-energy models and apply it to gain a detailed microscopic understanding across a family of cuprate superconducting materials in their parent undoped states. We uncover microscopic trends in the electron correlations and reveal the link between the material composition and magnetic energy scales through a many-body picture of excitation processes involving the buffer layers. Our work illustrates a path toward a quantitative and reliable understanding of more complex states of correlated materials at the ab initio many-body level.
Strongly correlated materials exhibit complex emergent phenomena -- such as unconventional high-temperature superconductivity -- that cannot be explained within a single or weakly-interacting particle description, making understanding their physics a central challenge in condensed matter physics. This thesis develops and applies novel approaches to strongly correlated electron systems, focusing on neural quantum states (NQS) and quantum simulation with cold atoms in optical lattices or Rydberg tweezer arrays. A key contribution of this work is the advancement of neural-network-based representations of quantum many-body states. By employing state-of-the-art network architectures like Transformers and combining them with physical constructions such as determinants, Pfaffians and Gutzwiller-projection, NQS are extended to simulate large two-dimensional fermionic single- and multi-band systems with high accuracy and beyond the capabilities of conventional methods. In addition, the thesis explores how quantum simulators based on ultracold atoms in optical lattices can be leveraged to study models directly relevant to strongly correlated materials -- e.g. the multi-band model of cuprate superconductors -- as well as proposes strategies to probe superconductivity in this setting. Furthermore, hybrid approaches that combine NQS with data from quantum simulators are developed. This synergy allows for improved optimization and direct comparison between theory and experiment. These methodological developments are applied to investigate two fundamental questions in high-temperature superconductivity: On the one hand, the work proposes a microscopic mechanism based on Feshbach resonances and tests this hypothesis extensively in a model system relevant to cuprates, nickelates and heavy fermion materials. On the other hand, it develops systematic approaches to derive effective low-energy models from more complex systems like multi-band models or electron-phonon coupled systems, shining light on the timely question which single-band models capture the physics of high-temperature superconductors like cuprate or nickelate materials. Overall, the thesis demonstrates how combining machine learning and quantum simulation provides powerful tools for understanding strongly correlated quantum matter.
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.
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.
The accurate first-principles description of strongly correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving compressed many-body Hamiltonians that maintain the essential physics of strongly correlated materials. The solution of these material-specific models is still exponentially difficult to generate on classical computers, but quantum algorithms allow for a significant speed-up in obtaining the ground states of these compressed Hamiltonians. Here, we demonstrate that using quantum algorithms to obtain the properties of downfolded Hamiltonians can indeed yield high-fidelity solutions. By combining ab initio downfolding and variational quantum eigensolvers, we correctly predict the antiferromagnetic state of one-dimensional cuprate Ca2CuO3, the excitonic ground state of monolayer WTe2, and the charge-ordered state of correlated metal SrVO3. Numerical simulations using a classical tensor network implementation of variational quantum eigensolvers allow us to simulate large models with up to 54 qubits and encompassing up to four bands in the correlated subspace, which is indicative of the complexity that our framework can address. Through these methods we demonstrate the potential of classical preoptimization and downfolding techniques for enabling efficient materials simulation using quantum algorithms.
Methods based on the many-body Green's function are generally accepted as the path forward beyond Kohn-Sham based density functional theory, in order to compute from first principles electronic structure of materials with strong correlations and excited-state properties in nano- and materials science. Here we present an efficient method to compute the screened Coulomb interactionW, the crucial and computationally most demanding ingredient in the GW method, within the framework of the all-electron Linearized Augmented Plane Wave method. We use the method to compute from first principles, within the constrained random phase approximation (c-RPA), the frequency-dependent screened Hubbard U-matrix defined for a Wannier basis in which we downfold the many-body Hamiltonian for La2CuO4, the canonical parent compound of several cuprate high-temperature superconductors. These results were computed at scale on the Cray XT5 at ORNL, sustaining 1.30 petaflop. We discuss the details of the algorithm and its implementation that allowed us to reach high efficiency and short time to solution on today's petaflop supercomputers.