长程相互作用量子模型的精确快速级数展开
Exact and fast series expansions for quantum models with long-range interactions
- Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡大学）
- University of Vienna（维也纳大学）
- Saarland University（萨尔兰大学）
- ETH Zürich（苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出图zeta方法，以确定性高精度计算替代蒙特卡洛，快速获得长程相互作用量子模型的级数展开，并应用于KTmSe$_2$，验证偶极相互作用模型。
AI中文摘要：
在过去十年中，基于链接簇方法的高阶级数展开已成为研究具有长程相互作用的带隙量子系统低能性质的重要工具。我们引入了一个确定性框架，消除了该方法的一个核心计算瓶颈。我们的图zeta方法用系统的高精度计算取代了对高维晶格求和进行昂贵且统计上有噪声的蒙特卡洛（MC）评估，该计算在标准桌面硬件上几分钟内即可给出级数系数。完整的动量依赖级数通过单次计算获得，从而能够在整个布里渊区内实现高分辨率的激发谱。基于配套论文[1]，该方法将图嵌入求和重新表述为图zeta函数，并将其分解为按树宽tw分类的块。低树宽块（tw≤2）允许基于Epstein zeta函数的闭式表达式，而高树宽块（tw>2）则使用张量网络桶消除进行评估。我们在1维、2维和3维中针对具有幂律相互作用的横向场伊辛模型对该方法进行了基准测试，以计算成本的一小部分重现了之前的MC结果，同时实现了更密集的参数采样。一个开源实现使该方法可直接应用于一般相互作用和大规模参数扫描。作为应用，我们比较了堆叠准二维横向场伊辛三角晶格反铁磁体KTmSe$_2$的微观相互作用模型，发现包含偶极相互作用的模型最能描述现有实验数据。因此，图zeta方法将高阶级数展开转变为一种实用且确定性的工具，用于对短程和长程量子物质进行快速的定量动量分辨建模。
英文摘要：
Over the past decade, high-order series expansions based on linked-cluster methods have become an important tool for studying low-energy properties of gapped quantum systems with long-range interactions. We introduce a deterministic framework that removes a central computational bottleneck of this method. Our graph zeta method replaces the costly and statistically noisy Monte Carlo (MC) evaluation of high-dimensional lattice sums by a systematic, high-precision computation that delivers series coefficients within minutes on standard desktop hardware. The full momentum-dependent series is obtained in a single calculation, enabling high-resolution excitation spectra throughout the Brillouin zone. Building on the companion paper [1], the method reformulates graph-embedding sums as graph zeta functions and decomposes them into blocks classified by their treewidth tw. Low-treewidth blocks (tw$\leq2$) admit closed expressions based on Epstein zeta functions, while higher-treewidth blocks (tw$>2$) are evaluated using tensor-network bucket elimination. We benchmark the approach for transverse-field Ising models with power-law interactions in 1d, 2d, and 3d, reproducing previous MC results at a fraction of the computational cost while enabling substantially denser parameter sampling. An open-source implementation makes the method directly applicable to general interactions and large parameter scans. As an application, we compare microscopic interaction models for the stacked quasi-2d transverse-field Ising triangular-lattice antiferromagnet KTmSe$_2$ and find that a model including dipolar interactions best describes existing experimental data. The graph zeta method thus turns high-order linked-cluster expansions into a practical and deterministic tool for fast quantitative momentum-resolved modeling of short- and long-range quantum matter.
