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arXiv · 2510.05647

Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems

Johnnie Gray·Gunhee Park·Glen Evenbly·Nicola Pancotti·Eirik F. Kjønstad·Garnet Kin-Lic Chan
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Abstract

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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Johnnie Gray, Gunhee Park, Glen Evenbly, Nicola Pancotti, Eirik F. Kjønstad, Garnet Kin-Lic Chan. 2025-10-07. Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems. https://doi.org/10.1103/r6mz-6q3g

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