Harnessing Locality for Scalable Strongly Correlated Electron Simulations

Materials-specific predictions of large, realistic molecules and materials with strong electron correlations have been a long-standing challenge in quantum chemistry. This dissertation addresses this challenge by leveraging three forms of physical and mathematical locality—in space, energy, and rank—to develop scalable, efficient, and accurate electronic structure methods. In Chapter 2, we use quantum embedding theory that exploits the spatial locality of electron correlations and reduces the computational cost of accurate correlated electronic structure methods, enabling accurate ab initio simulation of complicated correlated materials. In this work, we study Kondo physics, a prototypical many-body quantum phenomenon, with a full-cell extension of dynamical mean-field theory (DMFT). Our \textit{ab initio} simulation of the Kondo correlations systematically converges towards the exact zero-temperature limit, yielding material-specific Kondo temperatures that reproduce the subtle exponential trends observed experimentally and offer new insight into the underlying physics. Chapter 3 explores the locality in energy in lanthanide single-ion magnets. Their multi-reference ground and excited states are generally challenging to compute, but fortunately, the states that govern the spin dynamics are local in the energy spectrum. We develop a theoretical protocol to compute their spin Hamiltonian by sampling only relevant states in this reduced Hilbert space, and particularly, the single-reference states accessible by the efficient density functional theory. This method surpasses the prohibitive cost of calculating multi-reference eigenstates, and with its mean-field scaling, enables studying realistic magnets of unprecedentedly large size at an accuracy comparable to the previous state-of-the-art method. Chapter 4 focuses on the locality in the rank structure of reduced density matrices (RDMs). The 1- and 2-RDMs are the crucial ingredients in estimating energies and observables in many classical and quantum simulation methods. Their intrinsic low-rank structure makes them compressible and can be exploited to significantly reduce the measurement cost. We analyze both noiseless and noisy measurement scenarios, including shot-noise-limited quantum algorithms, and show that in the context of Gaussian (shot) noise, a low-rank approximate reconstruction of RDMs effectively removes the high-rank noises and reduces the measurement cost by orders of magnitude, therefore enabling larger-scale simulations.