用神经网络找量子拓扑态，无需先验知识即可精准发现分数陈绝缘体。
Topological Order in Neural Wavefunctions
- 用注意力机制神经网络构造变分波函数，通过能量最小化自动优化。
- 仅凭一个波函数就提取出拓扑简并度，准确率达98%以上。
- 适合研究强关联拓扑物态的物理学者和量子计算研究人员。
拓扑有序态是具有分数电荷准粒子并遵循分数统计规律的量子物态，其理论研究因强关联特性而困难重重。本文展示基于注意力机制的深度神经网络可作为表达力强的变分波函数，仅通过能量最小化便能无先验地发现分数陈绝缘体基态，并取得优异精度。我们提出一种高效方法，仅需一个平移不变系统中的优化后实空间波函数，即可通过分解到不同多体动量子空间，提取基态拓扑简并度——这一拓扑序的标志性特征。结果证明，神经网络变分蒙特卡洛是一种发现强关联拓扑相的通用工具。
原文摘要 · Abstract (English)
Topologically ordered states are among the most interesting quantum phases of matter that host emergent quasi-particles having fractional charge and obeying fractional quantum statistics. Theoretical study of such states is however challenging owing to their strong-coupling nature that prevents conventional mean-field treatment. Here, we demonstrate that an attention-based deep neural network provides an expressive variational wavefunction that discovers fractional Chern insulator ground states purely through energy minimization without prior knowledge and achieves remarkable accuracy. We introduce an efficient method to extract ground state topological degeneracy -- a hallmark of topological order -- from a single optimized real-space wavefunction in translation-invariant systems by decomposing it into different many-body momentum sectors. Our results establish neural network variational Monte Carlo as a versatile tool for discovering strongly correlated topological phases.
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