Tensor network investigation of the monomer-dimer model on the honeycomb lattice
Abstract
The monomer-dimer model is one of the most well-known unsolved lattice models. In this paper we study the monomer-dimer model on the honeycomb lattice using the tensor network method, in the case that the dimer and monomer activities are 1. The monomer-dimer configurations are exactly mapped into the ground states of the antiferromagnetic Ising model on the Kagomé lattice in the critical field Hex=4J, and the tensor network is constructed based on the local ground states of each Ising triangle. The VUMPS approach is employed to contract the tensor network, providing a high-precision result of the monomer-dimer problem. We also revisit the edge coloring problem on the honeycomb lattice and discuss its relationship to the monomer-dimer model. Finally we formulate the monomer-dimer problem in the language of the sixteen-vertex model, and discuss the non-integrability of the general monomer-dimer model and the integrability of the pure dimer model.
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BibTeX
@misc{li2026tensor,
title = {{Tensor network investigation of the monomer-dimer model on the honeycomb lattice}},
author = {De-Zhang Li and Jie Liu and Xin Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07899},
eprint = {2609.07899},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07899},
}
RIS
TY - UNPB
TI - Tensor network investigation of the monomer-dimer model on the honeycomb lattice
AU - De-Zhang Li
AU - Jie Liu
AU - Xin Wang
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07899
UR - https://arxiv.org/abs/2609.07899
AB - The monomer-dimer model is one of the most well-known unsolved lattice models. In this paper we study the monomer-dimer model on the honeycomb lattice using the tensor network method, in the case that the dimer and monomer activities are 1. The monomer-dimer configurations are exactly mapped into the ground states of the antiferromagnetic Ising model on the Kagomé lattice in the critical field H_ex=4J, and the tensor network is constructed based on the local ground states of each Ising triangle. The VUMPS approach is employed to contract the tensor network, providing a high-precision result of the monomer-dimer problem. We also revisit the edge coloring problem on the honeycomb lattice and discuss its relationship to the monomer-dimer model. Finally we formulate the monomer-dimer problem in the language of the sixteen-vertex model, and discuss the non-integrability of the general monomer-dimer model and the integrability of the pure dimer model.
ER -