We analyze the tensor network loop cluster expansion, introduced by G. Park et al. [Phys. Rev. B 112, 174310 (2025)] as a systematic correction to belief propagation, in the context of general quantum many-body problems. We provide numerical examples of the accuracy and practical applicability of the approach for the computation of ground-state observables for high bond dimension tensor networks, in two and three dimensions, with open and periodic boundary conditions, and for spin and fermion problems. We find that the contraction error converges approximately exponentially with cluster size, enabling accurate local observable and energy estimates for many systems where standard contraction methods are otherwise impractical.

Close

PrevNext

View figure in article

• Quantum spin models
• Cluster expansion
• Heisenberg model
• Hubbard model
• Tensor network methods