蜂窝格点上单体-二聚体模型的张量网络研究
Tensor network investigation of the monomer-dimer model on the honeycomb lattice
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中文总结 AI 辅助
本文用张量网络方法研究蜂窝格点上的单体-二聚体模型，通过映射到Kagomé反铁磁Ising模型并用VUMPS收缩，获得高精度结果，并探讨了与边着色及十六顶点模型的关系。
中文摘要 AI 辅助
单体-二聚体模型是最著名的未解格点模型之一。本文利用张量网络方法研究蜂窝格点上的单体-二聚体模型，其中二聚体和单体的活度均为1。单体-二聚体构型被精确映射到Kagomé格点上临界场$H_{\ m{ex}}=4J$中的反铁磁Ising模型的基态，张量网络基于每个Ising三角形的局部基态构建。采用VUMPS方法收缩张量网络，为单体-二聚体问题提供了高精度结果。我们还重新审视了蜂窝格点上的边着色问题，并讨论了其与单体-二聚体模型的关系。最后，我们将单体-二聚体问题表述为十六顶点模型的语言，并讨论了一般单体-二聚体模型的不可积性以及纯二聚体模型的可积性。
英文摘要
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 $H_{\rm{ex}}=4J$, 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.
发表机构
- Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）
- Department of Physics, City University of Hong Kong（香港城市大学物理系）
- City University of Hong Kong Shenzhen Research Institute（香港城市大学深圳研究院）
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