AI 中文总结
本文利用NQS与PEPS方法研究三角晶格Hofstadter-Hubbard模型，在实空间观测到自旋-电荷分离，小系统中存在正双电子结合能，验证了两类方法对强关联电子系统拓扑序等的诊断能力。
AI 中文摘要
最近，摩尔材料领域的实验已实现多种奇异量子相。在此背景下，Hofstadter-Hubbard模型被认为是可能承载手征自旋液体的候选体系。同时，二维多体费米子系统的计算方法近期取得了显著进展，这使得在真实二维几何中数值研究这一具有挑战性的模型成为现实。受这些进展的推动，我们使用带神经量子态（NQS）的变分蒙特卡洛方法和投影纠缠对态（PEPS），对三角晶格Hofstadter-Hubbard模型中假定的手征自旋液相展开研究。我们通过数值自旋泵浦模拟以及自旋和电荷的实时运动，直接在实空间中观测到了自旋-电荷分离。此外，在该模型中被推测存在的任意子超导语境下，我们发现小系统中存在正的双电子结合能，但随着系统尺寸增大，该结合能降至我们的数值分辨率以下。我们的工作证明，NQS和PEPS是强大的工具，能够相互交叉验证，用于诊断强关联电子系统中的拓扑序和分数化激发。
英文摘要
Recent experiments in moiré materials have enabled the realization of a variety of exotic quantum phases. In this context, the Hofstadter-Hubbard model has been proposed as a possible setting for hosting chiral spin liquid. Concurrently, significant progress has been recently made in the computational methods for two-dimensional many-body fermion systems, which makes numerically studying this challenging model a real possibility in genuine 2D geometry. Motivated by these advances, we investigate the putative chiral spin liquid phase in the triangular-lattice Hofstadter-Hubbard model using variational Monte Carlo with neural quantum states (NQS) and projected entangled pair states (PEPS). We observe spin-charge separation directly in real space through numerical spin-pumping simulation and real-time spin and charge motion. In addition, in the context of anyonic superconductivity conjectured in this model, we find a positive two-electron binding energy on small systems, but it decreases below our numerical resolution as the system size increases. Our work demonstrates NQS and PEPS as powerful tools, capable of cross-checking each other, for diagnosing topological order and fractionalized excitations in strongly correlated electronic systems.
Comments6 pages, 5 figures. 1 supplement
