Weatherly Shaun, Van Voorhis Troy
Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States.
J Chem Theory Comput. 2025 Aug 26;21(16):7818-7829. doi: 10.1021/acs.jctc.5c00725. Epub 2025 Aug 7.
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 and . 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 -; quasi-linear -; 2D and 3D -lattices; 2D ). 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.
张量网络（TNs）以及作用于其上的众多算法，在精确且高效地模拟强相互作用区域的量子多体系统方面取得了惊人的成功。在量子化学领域，史蒂文·怀特的密度矩阵重整化群（DMRG）作为首选的TN方法，仍然占据着核心地位。近几十年来，它取得了无数的理论和计算突破，但仍受一些持续存在的缺点的束缚，特别是缺乏 和 。在这里，我们提出了一个简单而通用的框架来规避这些问题：自洽嵌入密度矩阵重整化群（BE-DMRG），并对强关联分子系统（线性 -；准线性 -；二维和三维 -晶格；二维 ）的测试平台进行了数值验证，验证了其具有广延性和准精确的基态性质。跨越广泛的系统规模（10到200个轨道）和纠缠拓扑结构（从线性到高度非线性），我们证明了BE-DMRG对于传统DMRG实现难以企及的问题具有鲁棒性。此外，通过详细说明BE-DMRG相对于精确对角化的收敛行为，我们发现其与键维度的收敛速度明显快于传统DMRG，且同样可靠。最终，我们发现嵌入DMRG可能是怀特原始公式向更高维度的自然扩展，而无需高阶张量网络。更广泛地说，张量网络理论与量子嵌入框架的结合，可能成为研究强关联分子和材料的无比强大的工具。
