发表机构
School of Physics, Nankai University（南开大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究揭示数守恒冷却在平带制备中的失败机制，提出边界秩障碍与测量辅助恢复方法，并证明在特定条件下可恢复全局吸引并保持目标哈密顿量。
AI 中文摘要
当泡利不相容原理阻碍转移目标时，数守恒冷却可能无法制备相互作用的平带目标。我们在每个平带轨道一个粒子的顶点-边装饰图上研究这种失败。平带轨道格拉姆矩阵的切割块的秩限制了可以保持平坦的残余源方向的数量。对于没有哈密顿量项的子线性范围冷却，周期性装饰超立方晶格上的分离自旋域支持指数多的具有非零亮粒子密度的稳态。对于具有固定有限冷却范围的链，我们构造了一个物理的福克初始态，其与错误暗态的重叠与系统尺寸无关。这给出了在任何时刻都有效的保真度和亮密度界限。在更高维度中，裸重叠随边界面积衰减，而局部边界旋转在恒定电路深度内制备具有有限失败权重的态。当图和冷却目的地满足所述条件时，对所有紧凑亮模式的占据进行退相恢复了对铁磁目标的全局吸引。该结果允许保持目标的哈密顿量。强退相极限下的压缩动力学也保持吸引性，并在每个固定尺寸处具有正间隙。格拉姆计算、有限系统动力学和利奥维尔谱测试了分析结果。弱退相和粒子输运界限约束了制备时间，尽管最终收敛。
英文摘要
Number-conserving cooling can fail to prepare an interacting flat-band target when Pauli exclusion blocks its transfer destinations. We study this failure on vertex-edge decorated graphs at one particle per flat orbital. The rank of a cut block of the flat-orbital Gram matrix bounds the number of residual source directions that can remain flat. For sublinear-range cooling with no Hamiltonian term, separated spin domains on periodic decorated hypercubic lattices support exponentially many stationary states with a nonzero bright-particle density. For a chain with fixed finite cooling range, we construct a physical Fock initial state whose overlap with a wrong dark state is independent of system size. This gives fidelity and bright-density bounds valid at every time. In higher dimensions, the bare overlap decays with boundary area, while local boundary rotations prepare states with a finite failure weight in constant circuit depth. Dephasing the occupations of all compact bright modes restores global attraction to the ferromagnetic target when the graph and cooling destinations satisfy the stated conditions. The result allows Hamiltonians that preserve the target. The compressed dynamics in the strong-dephasing limit also remains attractive and has a positive gap at each fixed size. Gram calculations, finite-system dynamics, and Liouvillian spectra test the analytic results. Weak-dephasing and particle-transport bounds constrain the preparation time despite eventual convergence.
Comments12 pages, 4 figures; Supplemental Material: 22 pages, 1 figure, 1 table
