We present an efficient implementation of ab initio many-body quantum embedding and local correlation methods for infinite periodic systems through translational symmetry adapted interpolative separable density fitting, an approach that reduces the scaling of the calculations to only linear with the number of k-points. Employing this methodology, we compute correlated ground-state coupled cluster energies within density matrix embedding and local natural orbital correlation frameworks for both weakly and strongly correlated solids, using up to 1000 k-points. By extrapolating the local correlation domains and k-point sampling, we further obtain estimates of the full coupled cluster with singles, doubles, and perturbative triples ground-state energies in the thermodynamic limit.
We present an efficient implementation of ab initio many-body quantum embedding and local correlation methods for infinite periodic systems through translational symmetry adapted interpolative separable density fitting, an approach that reduces the scaling of the calculations to only linear with the number of k-points. Employing this methodology, we compute correlated ground-state coupled cluster energies within density matrix embedding and local natural orbital correlation frameworks for both weakly and strongly correlated solids, using up to 1000 k-points. By extrapolating the local correlation domains and k-point sampling, we further obtain estimates of the full coupled cluster with singles, doubles, and perturbative triples ground-state energies in the thermodynamic limit.
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.
We describe an efficient quantum embedding framework for realistic ab initio density matrix embedding theory (DMET) calculations in solids. We discuss in detail the choice of orbitals and mapping to a lattice, treatment of the virtual space and bath truncation, and the lattice-to-embedded integral transformation. We apply DMET in this ab initio framework to a hexagonal boron nitride monolayer, crystalline silicon, and nickel monoxide in the antiferromagnetic phase, using large embedded clusters with up to 300 embedding orbitals. We demonstrate our formulation of ab initio DMET in the computation of ground-state properties such as the total energy, equation of state, magnetic moment, and correlation functions.
The transcorrelated (TC) method dramatically accelerates the convergence of correlated calculations toward the complete-basis-set (CBS) limit by folding a Jastrow correlator into the Hamiltonian via a similarity transformation, incorporating the electron--electron cusp into the effective interaction. We make the TC framework practical for large systems and flexible, multi-center correlators by compressing the grid-evaluated TC integrals with the interpolative separable density-fitting (ISDF) approximation, combined with the effective two-body (xTC) treatment of the three-body operator. This low-rank representation reduces storage and integration costs by orders of magnitude, and a multi-GPU implementation with automatic differentiation of the correlator makes the construction routine for large basis sets. We demonstrate the resulting ISDF-xTC-CCSD method on the linear hydrogen chain, reaching the joint thermodynamic and CBS limits with basis sets up to cc-pV5Z in agreement with state-of-the-art many-body references to within about 1~mHa/atom, and on the benzene ground-state energy with up to 1200 orbitals (cc-pCV5Z), where the method attains state-of-the-art accuracy at the coupled cluster singles and doubles level and its CBS extrapolation is markedly more robust than that of conventional coupled-cluster methods.
We developed a periodic version of density matrix embedding theory, DMET, with which it is possible to perform electronic structure calculations on periodic systems and compute the band structure of solid-state materials. Electron correlation can be captured by means of a local impurity model using various wave function methods, such as full configuration interaction, coupled cluster, and multiconfigurational methods. The method is able to describe not only the ground-state energy but also the quasiparticle band picture via the real space-momentum space implementation. We investigate the performance of periodic DMET in describing the ground-state energy as well as the electronic band structure for one-dimensional solids. Our results show that DMET is in good agreement with other many-body techniques at a cheaper computational cost. We anticipate that periodic DMET can be a promising first principle method for strongly correlated materials.
Low-Scaling algorithms for GW and constrained random phase approximation using symmetry-adapted interpolative separable density fitting
We present low-scaling algorithms for GW and constrained random phase approximation based on a symmetry-adapted interpolative separable density fitting (ISDF) procedure that incorporates the space-group symmetries of crystalline systems. The resulting formulations scale cubically with respect to system sizes and linearly with the number of k-points, regardless of the choice of single-particle basis and whether a quasiparticle approximation is employed. We validate these methods through comparisons with published literature and demonstrate their efficiency in treating large-scale systems through the construction of downfolded many-body Hamiltonians for carbon dimer defects embedded in hexagonal boron nitride supercells. Our work highlights the efficiency and general applicability of ISDF in the context of large-scale many-body calculations with k-point sampling beyond density functional theory.
We present low-scaling algorithms for GW and constrained random phase approximation based on a symmetry-adapted interpolative separable density fitting (ISDF) procedure that incorporates the space-group symmetries of crystalline systems. The resulting formulations scale cubically, with respect to system size, and linearly with the number of k -points, regardless of the choice of single-particle basis and whether a quasiparticle approximation is employed. We validate these methods through comparisons with published literature and demonstrate their efficiency in treating large-scale systems through the construction of downfolded many-body Hamiltonians for carbon dimer defects embedded in hexagonal boron nitride supercells. Our work highlights the efficiency and general applicability of ISDF in the context of large-scale many-body calculations with k -point sampling beyond density functional theory.