发表机构
The University of Texas at Dallas（德克萨斯大学达拉斯分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对含k-局域全对相互作用的非厄米自旋系综，解析追踪了主导本征值，发现不同无序下主导本征态会在异常态与谱体态间切换，还将非厄米演化映射到受监控量子系统的后选择轨迹，关联了谱机制与测量诱导转变。
AI 中文摘要
非厄米系统的长时间态由虚部最大的本征值决定。在相互作用多体系统中，该本征值通常无法通过解析方法追踪，且其选取态的性质也未知。我们构建了一个含L个自旋的非厄米自旋系综，具有精确的k-局域全对相互作用，其中该主导本征值可从清洁极限到无序区进行解析追踪。无序会在孤立的谱异常值与多体谱体的边缘之间产生竞争。我们研究三种情况：纯反厄米无序、纯厄米无序以及等强度混合无序。对于纯反厄米和混合无序，我们表明，当谱体在虚部上超过异常值时，主导本征态会从具有低纠缠和魔性（非稳定度）的异常态切换到具有显著更大纠缠和魔性的谱体态，且两者在同一阈值处发生变化。当k远大于√L时，谱体具有尖锐的谱边缘，转变阈值遵循闭式形式；而当k远小于√L时，谱尾会将转变拓宽为交叉。纯厄米无序则提供了无异常值到谱体切换的对比情况。最后，我们将非厄米演化精确映射到受监控量子系统的后选择轨迹，将该谱机制与测量诱导转变关联起来。
英文摘要
The long-time state of a non-Hermitian system is determined by the eigenvalue with the largest imaginary part. In interacting many-body systems this eigenvalue usually cannot be tracked analytically, and the character of the state it selects is unknown. We construct a non-Hermitian spin ensemble of $L$ spins with exactly $k$-local all-to-all interactions, in which this dominant eigenvalue can be tracked analytically from the clean limit into the disordered regime. Disorder produces a competition between an isolated spectral outlier and the edge of a many-body spectral bulk. We study three cases: purely anti-Hermitian disorder, purely Hermitian disorder, and mixed disorder of equal strength. For purely anti-Hermitian and mixed disorder, we show that when the bulk overtakes the outlier in imaginary part, the dominant eigenstate switches from an outlier state with low entanglement and magic (nonstabilizerness) to a bulk state with substantially larger entanglement and magic, with both changing at the same threshold. For $k \gg \sqrt{L}$ the bulk has a sharp spectral edge and the transition thresholds follow in closed form, while for $k \ll \sqrt{L}$ spectral tails broaden the transition into a crossover. Purely Hermitian disorder provides a contrasting case with no outlier-to-bulk switching. Finally, we map the non-Hermitian evolution exactly onto postselected trajectories of a monitored quantum system, connecting this spectral mechanism to measurement-induced transitions.
Comments35 pages, 18 figures
