AI 中文总结
研究通过COMPASS框架弥合挫折与非厄米性，结合自适应架构、双正交优化和对称性感知建模，能直接研究NH多体系统。应用于受挫磁性系统，发现能隙挫折可屏蔽光谱不稳定性，复化耦合产生新拓扑结构，即恶魔环。
AI 中文摘要
在这项工作中，我们引入了一种基于双正交自适应递归神经量子态的渐进和自适应状态搜索的互补优化方法（COMPASS）。我们的方法将自适应自回归架构与双正交变分蒙特卡罗方案以及在能量和方差最小化之间交替的互补优化方案相结合。这使得能够稳定收敛到基态本征对，同时通过精确的自回归生成避免马尔可夫链采样。我们证明，对于宇称时间（PT）对称哈密顿量，无约束的复近似在优化过程中甚至在未破缺相中也会自发打破PT对称性，导致虚假的虚能量。另一方面，实值近似自然地将优化约束到正确的物理流形。相反，对于没有对称性保护和复谱的一般非厄米（NH）哈密顿量，复近似对于捕获复基态性质至关重要。我们的结果表明，基于物理的近似选择对于可靠的NH模拟至关重要。通过结合自适应架构、双正交优化和对称性感知建模，该框架能够直接研究一维和二维NH多体系统，而无需厄米嵌入或绝热延续。将此框架应用于具有受挫磁性的系统，我们表明能隙挫折为NH光谱不稳定性提供了定量屏蔽，挫折能隙为PT对称性破缺设定了临界阈值。此外，使挫折耦合本身复化会产生一个由复耦合相位控制的新的拓扑非平凡的恶魔能级交叉网络，这没有厄米类似物。我们将NH受挫系统中的这种新颖光谱拓扑称为恶魔环。
英文摘要
In this work, we introduce a complementary optimization method for progressive and adaptive state search (COMPASS) based on biorthogonal adaptive recurrent neural quantum states. Our approach combines an adaptive autoregressive architecture with a biorthogonal variational Monte Carlo scheme as well as a complementary optimization scheme that alternates between energy and variance minimization. This enables the stable convergence to ground-state eigenpairs, while avoiding Markov chain sampling through exact autoregressive generation. We demonstrate that for parity-time(PT)-symmetric Hamiltonians, unconstrained complex ansatze can spontaneously break PT symmetry during optimization, even in the unbroken phase, leading to spurious imaginary energies. Real-valued ansatze, on the other hand, naturally constrain the optimization to the correct physical manifold. Conversely, for generic non-Hermitian (NH) Hamiltonians without symmetry protection and complex spectra, complex ansatze are essential for capturing complex ground-state properties. Our results establish that physically-informed ansatz selection is crucial for reliable NH simulations. By combining adaptive architectures, biorthogonal optimization, and symmetry-aware modeling, this framework enables a direct study of 1D and 2D NH many-body systems without Hermitian embeddings or adiabatic continuation. Applying this framework to systems with frustrated magnetism, we show that gap frustration provides a quantitative shield against NH spectral instability, with the frustration gap setting a critical threshold for PT-symmetry breaking. Also, complexifying the frustration coupling itself generates a new topologically nontrivial network of diabolic level crossings, controlled by the phase of the complex coupling, that has no Hermitian analog. We term this novel spectral topology in NH frustrated systems the diabolic ring.
