Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems

2025/10/07 by Gray, Johnnie, Park, Gunhee, Evenbly, Glen +3 · 3 citations
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2510.05647

Abstract

We analyze the tensor network loop cluster expansion, introduced in arXiv:2504.07344 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.

Citations

• Beyond Belief Propagation: Cluster-Corrected Tensor Network Contraction with Exponential Convergence
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Fermionic tensor network contraction for arbitrary geometries
• Loop Series Expansions for Tensor Networks
• Response properties in phaseless auxiliary field quantum Monte Carlo
• One-step replica symmetry breaking in the language of tensor networks
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• A practical introduction to tensor networks: Matrix product states and projected entangled pair states
• A Cluster-Cumulant Expansion at the Fixed Points of Belief Propagation
• The density-matrix renormalization group in the age of matrix product states
• Grassmann tensor network states and its renormalization for strongly correlated fermionic and bosonic states
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• Density-matrix algorithms for quantum renormalization groups

Cited by

• Resolving Structure in Prethermal Floquet Dynamics with Precision Quantum Computation
• Leveraging Symmetry Merging in Pauli Propagation
• Partitioned Expansions for Approximate Tensor Network Contractions
• Beyond Belief Propagation: Cluster-Corrected Tensor Network Contraction with Exponential Convergence

Related

• Beyond Belief Propagation: Cluster-Corrected Tensor Network Contraction with Exponential Convergence
• Tensor Networks: a quantum-information perspective on numerical renormalization groups
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Loop Series Expansions for Tensor Networks
• Partitioned Expansions for Approximate Tensor Network Contractions