AI 中文总结
该研究针对强关联拓扑物质和量子模拟中稳定非阿贝尔分数量子霍尔相的挑战，引入可微框架，通过优化霍尔丹赝势，在球面几何中获得稳健赝势分布，稳定了Pfaffian拓扑相，建立了设计非阿贝尔拓扑序的通用框架。
AI 中文摘要
在强关联拓扑物质和量子模拟中，设计能稳定非阿贝尔分数量子霍尔相的相互作用是一项核心挑战。我们引入了一个用于逆哈密顿量设计的可微框架，通过基于梯度的精确对角化来优化霍尔丹赝势以稳定目标分数量子霍尔相。在球面几何中，将霍尔丹赝势视为变分参数并在基于JAX的精确对角化框架中进行优化。通过直接最大化多体基态与摩尔-里德态之间的重叠，我们获得了一个稳健的赝势分布，对于多达\(N_e = 12\)的系统，其Pfaffian重叠超过\(99\%\)，比传统库仑相互作用有显著改进。对中性激发谱和轨道纠缠谱的分析进一步证实了优化后的相互作用稳定了Pfaffian拓扑相。我们的结果表明，三体Pfaffian母哈密顿量的基本特征可以有效地编码在适当设计的两体相互作用中。此外，它们确定了一个几乎通用的指数衰减赝势分布，该分布稳定了Pfaffian相，并建立了一个在量子模拟中设计非阿贝尔拓扑序的通用框架。
英文摘要
Engineering interactions that stabilize non-Abelian fractional quantum Hall phases is a central challenge in strongly correlated topological matter and quantum simulation. We introduce a differentiable framework for inverse Hamiltonian design, in which Haldane pseudopotentials are optimized by gradient-based exact diagonalization to stabilize target fractional quantum Hall phases. In spherical geometry, the Haldane pseudopotentials are treated as variational parameters and optimized in a JAX-based exact-diagonalization framework. By directly maximizing the overlap between the many-body ground state and the Moore-Read state, we obtain a robust pseudopotential profile that has Pfaffian overlaps exceeding $99\%$ for systems up to $N_e=12$, substantially improving over conventional Coulomb interactions. Analyses of the neutral excitation spectrum and orbital entanglement spectrum further confirm that the optimized interaction stabilizes the Pfaffian topological phase. Our results demonstrate that essential features of the three-body Pfaffian parent Hamiltonian can be effectively encoded in a suitably designed two-body interaction. Furthermore, they identify a nearly universal exponentially decaying pseudopotential profile that stabilizes the Pfaffian phase and establishes a general framework toward engineering non-Abelian topological order in quantum simulation.
Comments9 pages, 10 figures
