用神经量子态求解二维掺杂哈伯德模型，发现条纹相变。
Solving the Hubbard model with Neural Quantum States
- 基于Transformer架构的神经量子态，高效优化强关联体系。
- 首次在半填充下确认存在条纹序，与铜氧化物实验一致。
- 不同注意力头可编码多尺度关联，适合研究长程纠缠。
神经量子态（NQS）的快速发展使其成为研究量子多体系统的重要框架。本文利用先进的基于Transformer的架构并开发高效优化算法，实现了对掺杂二维（2D）哈伯德模型的当前最优结果，该模型被认为是高温超导性的最小模型。有趣的是，我们发现NQS中的不同注意力头可直接编码不同尺度的相关性，从而能够捕捉强关联体系中的长程相关性和纠缠。借助这些进展，我们确认了在包含最近邻跳变的二维哈伯德模型中，基态存在半填充条纹相，与铜氧化物材料的实验观测一致。本工作确立了NQS作为解决复杂多费米子系统的关键工具。
原文摘要 · Abstract (English)
The rapid development of neural quantum states (NQS) has established it as a promising framework for studying quantum many-body systems. In this work, by leveraging the cutting-edge transformer-based architectures and developing highly efficient optimization algorithms, we achieve the state-of-the-art results for the doped two-dimensional (2D) Hubbard model, arguably the minimum model for high-Tc superconductivity. Interestingly, we find different attention heads in the NQS ansatz can directly encode correlations at different scales, making it capable of capturing long-range correlations and entanglements in strongly correlated systems. With these advances, we establish the half-filled stripe in the ground state of 2D Hubbard model with the next nearest neighboring hoppings, consistent with experimental observations in cuprates. Our work establishes NQS as a powerful tool for solving challenging many-fermions systems.
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