AI 中文总结
该研究以传播复杂性为探针，分析扩展与长程AAH模型中量子猝灭的特性，通过Lanczos系数等识别迁移边相变，揭示不同相区猝灭的系数行为差异。
AI 中文摘要
我们研究了扩展与长程Aubry-Andre-Harper（AAH）模型中量子猝灭的传播复杂性，涵盖存在和不存在迁移边的区域。特别地，在支持能量依赖迁移边的扩展AAH模型中，我们证明了当猝灭后的准周期势跨越与初始本征态能量相关的迁移边时，长时间平均传播复杂性表现出非解析行为，从而可准确识别迁移边相变。该行为得到局域态密度传播的支持。我们进一步推导了准周期势消失和强极限之间猝灭的矩及对应Lanczos系数的解析表达式。Lanczos系数的行为取决于迁移边的存在与否：它们在Krylov基矢指数上呈现初始平台后衰减，这与无迁移边的常规AAH模型的近似恒定行为形成对比。对于长程（LR）跳跃，从局域相到扩展相的猝灭过程中，系数随Krylov基矢指数衰减，而反向猝灭时系数与AAH结果一致。
英文摘要
We investigate the spread complexity of quantum quenches in generalized and long-range Aubry-Andre-Harper (AAH) models, encompassing regimes with and without mobility edges. In particular, in the generalized AAH models supporting energy-dependent mobility edges, we demonstrate that the long-time averaged spread complexity exhibits nonanalytic behavior when the post-quench quasiperiodic potential crosses the mobility edge associated with the energy of the initial eigenstate, thereby accurately identifying the mobility-edge transition. Such a behavior is supported by the spreading of local density of states. We further derive analytical expressions for the moments and the corresponding Lanczos coefficients for quenches between the limits of vanishing and strong quasiperiodic potentials. The Lanczos coefficients display qualitatively distinct behavior depending on the presence of mobility edges - they exhibit an initial plateau followed by a decay with the Krylov basis index, in contrast to the nearly constant behavior of the conventional AAH model without mobility edges. For LR hopping, the coefficients decay with the Krylov basis index for quenches from the localized to the extended phase, while they coincide with the AAH results for quenches in the opposite direction.
Comments11 pages, 8 figures
