Low-scaling algorithms for many-body electronic structure and downfolding for quantum embedding*

Quantum embedding has become one of the most successful techniques for materials simulations due to its multilayer treatments for different physical scales. 

Aside from the need of efficient solvers for the strongly correlated subspace, constructing a material-specific low-energy Hamiltonian beyond density functional theory (DFT) requires an efficient many-body method for the weakly correlated environment. In this talk, I will report our recent efforts on the low-scaling algorithms for many-body electronic structure and downfolding based on tensor hypercontraction (THC). THC is a systematically controlled compression technique for generic many-body Hamiltonians in any canonical basis. The resulting representation of the many-body Hamiltonians exhibits desired separability in the orbital and k-points indices which leads to the constructions of low-scaling algorithms for the following many-body calculations. We demonstrate the applicability and efficiency of THC in the context of downfolding procedures, including GW electronic structure and constrained RPA. The efficiency of these THC-based many-body methods provides a route for constructing low-energy Hamiltonian beyond DFT for large-scale systems.