AI 中文总结
该研究提出ChernFormer模型，结合费米子Transformer与Chern-Simons相位，可同时描述玻色凝聚体与手性拓扑物质，经基准测试能准确恢复相关涡旋结构，为两类物质提供统一变分框架。
AI 中文摘要
能否用同一个神经波函数同时描述玻色凝聚体和手性拓扑液体？我们提出ChernFormer，它结合了费米子Transformer与固定Chern-Simons相位，该相位会为每一对粒子附着一个统计涡旋。每个因子在交换时会变号，因此它们的乘积恰好是玻色子。固定相位会改变统计特性但不改变概率，使得每个玻色子学习问题都等价于具有相同近似误差和重叠度的费米子问题。若容量足够，ChernFormer可在固定粒子数的平面上近似任意可归一化的玻色子波函数。有限且平滑的网络在粒子相遇时仍会消失，不过这个接触空穴可缩小，同时波函数和凝聚体份额趋近于无节点凝聚体的对应值。遵循\uc110azaryan等人2025年提出的“干草堆中的针”目标重构基准，我们在Kalmeyer-Laughlin基态及其前两个手性边缘态上测试ChernFormer。重叠曲线在所有采样的最大尺寸下均接近1，而当N=20时，所有三个态的独立振幅和相位图都能恢复局域Laughlin涡旋和集体边缘涡旋。相比之下，由相同逐粒子因子构成的连续非零乘积会遗漏这些基本边缘部分。因此，ChernFormer为传统玻色子序和手性拓扑物质提供了一种变分表述语言。
英文摘要
Can one neural wave function describe both a Bose condensate and a chiral topological liquid? We introduce ChernFormer, which combines a fermionic transformer with a fixed Chern-Simons phase that attaches one statistical vortex to every particle pair. Each factor changes sign under exchange, so their product is exactly bosonic. The fixed phase changes statistics but not probability, making every bosonic learning problem equivalent to a fermionic one with the same approximation error and overlap. With enough capacity, ChernFormer can approximate any normalizable bosonic wave function on the plane at fixed particle number. A finite, smooth network still vanishes when particles meet, yet this contact hole can shrink while the wave function and condensate fraction approach those of a nodeless condensate. Following the needle-in-a-haystack target-reconstruction benchmark introduced in \cite{NazaryanGaggioliTengFu2025}, we test ChernFormer on the Kalmeyer--Laughlin ground state and its first two chiral edge states. The overlap curves stay close to unity through their largest sampled sizes, while independent amplitude and phase maps at $N=20$ for all three states recover both local Laughlin vortices and the collective edge vortex. By contrast, a continuous, nonzero product of identical particle-wise factors misses these elementary edge sectors. ChernFormer therefore provides one variational language for conventional bosonic order and chiral topological matter.
Comments12 pages, 4 figures
