arXiv:2601.04104cond-mat.str-elcs.LG2026-01被引 3

用对称性保持的神经网络构建通用晶格力场模型,实现高效准确的多体动力学模拟。

Equivariant Neural Networks for Force-Field Models of Lattice Systems

  • 基于等变神经网络直接嵌入晶格系统的离散对称性,无需手工设计特征。
  • 在方格子霍尔斯坦模型上实现的力场模型成功捕捉了对称性破缺相的介观演化过程。
  • 适合研究电子-晶格耦合系统中微观机制与宏观动态行为的关联,尤其适用于新物态探索。

机器学习力场可在显著降低计算成本的同时实现接近第一性原理精度的大规模模拟。近期研究已将机器学习力场扩展至包含电子与结构或磁性自由度耦合的凝聚态晶格模型的绝热动力学模拟。然而,多数现有方法依赖于人工设计的对称性感知描述符,其构造常具有系统特异性,限制了通用性和跨不同晶格哈密顿量的可迁移性。本文提出一种基于等变神经网络(ENNs)的对称性保持框架,实现了从动态变量局部构型到晶格哈密顿量对应局域受力的通用、数据驱动映射。与针对分子系统设计的连续欧几里得对称性等变架构不同,本方法直接将晶格模型固有的离散点群和内部对称性嵌入神经网络表示中。以方格子霍尔斯坦模型为例,我们构建了一个基于ENNs的力场模型,该模型在大规模动力学模拟中精确再现了对称性破缺相的介观演化过程,验证了晶格等变架构在连接微观电子过程与凝聚态晶格系统涌现动态行为方面的有效性。

原文摘要 · Abstract (English)

Machine-learning (ML) force fields enable large-scale simulations with near-first-principles accuracy at substantially reduced computational cost. Recent work has extended ML force-field approaches to adiabatic dynamical simulations of condensed-matter lattice models with coupled electronic and structural or magnetic degrees of freedom. However, most existing formulations rely on hand-crafted, symmetry-aware descriptors, whose construction is often system-specific and can hinder generality and transferability across different lattice Hamiltonians. Here we introduce a symmetry-preserving framework based on equivariant neural networks (ENNs) that provides a general, data-driven mapping from local configurations of dynamical variables to the associated on-site forces in a lattice Hamiltonian. In contrast to ENN architectures developed for molecular systems -- where continuous Euclidean symmetries dominate -- our approach aims to embed the discrete point-group and internal symmetries intrinsic to lattice models directly into the neural-network representation of the force field. As a proof of principle, we construct an ENN-based force-field model for the adiabatic dynamics of the Holstein Hamiltonian on a square lattice, a canonical system for electron-lattice physics. The resulting ML-enabled large-scale dynamical simulations faithfully capture mesoscale evolution of the symmetry-breaking phase, illustrating the utility of lattice-equivariant architectures for linking microscopic electronic processes to emergent dynamical behavior in condensed-matter lattice systems.

力场模型等变网络晶格系统电子-晶格耦合

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