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MON: Monday Contributed Sessions
MON 23: Poster Session: Fundamental Aspects and Model Systems
MON 23.33: Poster
Monday, September 8, 2025, 18:30–20:30, ZHG Foyer 1. OG
DMRG on arbitrary geometries using Belief Propagation — •Hendrik Kühne3 and Christian B. Mendl1,2 — 1School of Computation, Information and Technology, Technical University of Munich — 2Munich Center for Quantum Science and Technology — 3School of Natural Sciences, Technical University of Munich
Tensor networks have recently attracted much attention as a powerful tool for modeling systems in quantum many-body physics. Their contraction is a significant challenge however, especially in highly connected networks, as memory requirements become prohibitive and the optimal contraction order is increasingly hard to find. The belief propagation algorithm has emerged as an alternative to exact contraction. It offers great flexibility, being completely independent of the geometry in question, however its accuracy suffers in the presence of loops. On the other hand, in Quantum Chemistry, the DMRG algorithm is regarded as the gold standard in solving the ground state problem. Its behavior is well-understood in 1D, however maintaining the necessary canonical forms in higher dimensions becomes increasingly complex. This work proposes to combine Belief Propagation and DMRG, thereby extending DMRG to higher dimensions and arbitrary system geometries. We demonstrate the viability of BP-DMRG on the transverse-field Ising model, where it yields ground states reliably with high fidelity. We also discuss limitations that we incur by using belief propagation, and possible future directions for improving the accuracy and controllability of BP-DMRG.
Keywords: Belief Propagation; DMRG; Quantum Chemistry; Tensor Networks