用等变归一化流模拟霍伯德模型，解决传统方法的采样偏差问题。
Simulating the Hubbard Model with Equivariant Normalizing Flows
- 设计等变归一化流学习霍伯德模型的玻尔兹曼分布
- 生成独立同分布样本，显著改善采样效率与准确性
- 适合研究碳纳米材料电子结构的物理学家和算法开发者
生成模型，尤其是归一化流，在统计力学、对撞机物理和格点场论等多个物理领域中表现出色，能够准确学习概率分布。在格点场论中，归一化流已成功用于学习玻尔兹曼分布，实现热力学可观测量的直接估计以及生成独立同分布（i.i.d.）配置。本文首次证明，归一化流可用于学习霍伯德模型的玻尔兹曼分布。该模型广泛用于研究石墨烯及其它碳纳米材料的电子结构。当前主流数值模拟方法如混合蒙特卡洛（HMC）常面临遍历性问题，可能导致物理可观测量的偏差估计。我们的数值实验表明，利用归一化流生成i.i.d.样本可有效缓解此类问题。
原文摘要 · Abstract (English)
Generative models, particularly normalizing flows, have shown exceptional performance in learning probability distributions across various domains of physics, including statistical mechanics, collider physics, and lattice field theory. In the context of lattice field theory, normalizing flows have been successfully applied to accurately learn the Boltzmann distribution, enabling a range of tasks such as direct estimation of thermodynamic observables and sampling independent and identically distributed (i.i.d.) configurations. In this work, we present a proof-of-concept demonstration that normalizing flows can be used to learn the Boltzmann distribution for the Hubbard model. This model is widely employed to study the electronic structure of graphene and other carbon nanomaterials. State-of-the-art numerical simulations of the Hubbard model, such as those based on Hybrid Monte Carlo (HMC) methods, often suffer from ergodicity issues, potentially leading to biased estimates of physical observables. Our numerical experiments demonstrate that leveraging i.i.d.\ sampling from the normalizing flow effectively addresses these issues.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。