PreprintarXiv licencearXiv
CTMRG as a tensor-network message-passing algorithm
Abstract
We formulate the corner transfer matrix equations, and the corner transfer matrix renormalization group built on them, as a set of local equations on general planar graphs. These equations depend only on the local subgraphs of the planar graph and are glued together consistently to describe the whole graph. Solving them yields message tensors and corner matrices, which can be used to construct an MPS environment for any connected subgraph. We test the proposed equations on the ferromagnetic Ising model, on a variety of infinite lattices (including hyperbolic ones) and on finite graphs, and find systematic improvement over belief propagation.
Related
- Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentials
- Learning to Decode Concatenated Quantum Codes with Hierarchical Message Passing
- Thermodynamic characterization of message-passing: Framework and initial study
- Exact solutions for models of evolving clustered networks with addition and deletion via age-resolved message passing
- Projective Geometric Algebra Graph Neural Networks: Edge-Modulated Message Passing via the Geometric Product
BibTeX
@misc{lukin2026ctmrg,
title = {{CTMRG as a tensor-network message-passing algorithm}},
author = {Illia Lukin and Andrii Sotnikov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00631},
eprint = {2610.00631},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00631},
}
RIS
TY - UNPB
TI - CTMRG as a tensor-network message-passing algorithm
AU - Illia Lukin
AU - Andrii Sotnikov
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00631
UR - https://arxiv.org/abs/2610.00631
AB - We formulate the corner transfer matrix equations, and the corner transfer matrix renormalization group built on them, as a set of local equations on general planar graphs. These equations depend only on the local subgraphs of the planar graph and are glued together consistently to describe the whole graph. Solving them yields message tensors and corner matrices, which can be used to construct an MPS environment for any connected subgraph. We test the proposed equations on the ferromagnetic Ising model, on a variety of infinite lattices (including hyperbolic ones) and on finite graphs, and find systematic improvement over belief propagation.
ER -