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arxiv: 2510.05647 · v3 · submitted 2025-10-07 · 🪐 quant-ph

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Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems

Eirik F. Kj{\o}nstad, Garnet Kin-Lic Chan, Glen Evenbly, Gunhee Park, Johnnie Gray, Nicola Pancotti

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classification 🪐 quant-ph
keywords clusterproblemstensorcontractionloopmany-bodynetworkquantum
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We analyze the tensor network loop cluster expansion, introduced in [G. Park, J. Gray, and G. K.-L. Chan, 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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Algorithmic Locality via Provable Convergence in Quantum Tensor Networks

    quant-ph 2026-04 unverdicted novelty 8.0

    For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affe...

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    quant-ph 2026-04 conditional novelty 8.0

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    quant-ph 2026-04 unverdicted novelty 5.0

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