The Embedded Density Matrix Renormalization Group: Size-Extensive and Quasi-Exact for Nonlinear Quantum Chemistry

Tensor networks (TNs) and the breadth of algorithms acting on them have seen astounding success in simulating quantum many-body systems in the strongly interacting regime with both accuracy and efficiency. In the context of quantum chemistry, Steven White’s density matrix renormalization group (DMRG) continues to take center stage as the TN method of choice, seeing countless theoretical and computational breakthroughs in recent decades yet remaining fettered by a few persistent shortcomings, notably, a lack of size-extensivity and quasi-exactness. Here, we present a simple yet versatile framework for circumventing these issues: the bootstrap embedded density matrix renormalization group (BE-DMRG), and numerically validate its size-extensive and quasi-exact ground-state properties for a test bed of strongly correlated molecular systems (linear H-chains; quasi-linear E-polyacetylene; 2D and 3D H-lattices; 2D arene flakes). Spanning a breadth of system sizes (10 to 200 orbitals) and entanglement topologies (linear to highly nonlinear), we demonstrate the robustness of the BE-DMRG for problems far beyond the reach of conventional DMRG implementations. Furthermore, by detailing BE-DMRG convergence behavior with respect to exact diagonalization, we find the rate of convergence with bond dimension to be significantly faster than, yet just as reliable as, that of conventional DMRG. Ultimately, we find that the embedded DMRG might serve as a natural extension of White’s original formulation to higher dimensions without the need for higher-order tensor networks. The coupling of tensor network theories to the framework of quantum embedding, more broadly, may become an incomparably powerful tool for the study of strongly correlated molecules and materials.