AI 中文总结
本文通过精确弱耦合锚点与量子蒙特卡洛模拟，追踪吸引性Hubbard双层模型中集体激发从单粒子杂化到对超交换的BCS-BEC渡越，揭示其哈密顿敏感性演化规律。
AI 中文摘要
集体激发可以在产生它们的微观自由度发生深刻变化时存活下来。我们从一个精确的弱耦合杂化锚点出发，追踪一个层奇对称的集体响应，进入吸引性Hubbard双层模型的配对区域，并发现其哈密顿敏感性以一种与从单粒子层间杂化向集体对超交换渡越一致的方式演化。在弱耦合下，对于相同的隧穿耦合层，一个精确恒等式将相对相位高斯核的零点固定在$2t_h$处，与层内跳跃无关。无符号行列式量子蒙特卡洛方法揭示了无需解析延拓的相互作用驱动的多体谱标度软化，而高斯响应理论提供了连续的极点解释，并展示了从层密度到相对对相位特征的转变。在配对区域，特征响应标度获得了对层内跳跃的逐渐增强的分数敏感性，以及部分朝向$1/U$定律的相互作用依赖性。这些结果展示了如何在一个费米子到复合玻色子渡越过程中追踪集体激发，同时约束其微观驱动力的变化。
英文摘要
Collective excitations can survive profound changes in the microscopic degrees of freedom that generate them. We track a layer-odd collective response from an exact weak-coupling hybridisation anchor into the paired regime of an attractive Hubbard bilayer and find that its Hamiltonian sensitivities evolve in a manner consistent with a crossover from single-particle interlayer hybridisation towards collective pair superexchange. At weak coupling, an exact identity for identical tunnel-coupled layers fixes a relative-phase Gaussian kernel zero at $2t_h$, independent of the intralayer hopping. Sign-free determinant quantum Monte Carlo reveals an interaction-driven softening of the many-body spectral scale without analytic continuation, while Gaussian response theory supplies the continuous pole interpretation and shows a shift from layer-density to relative-pair-phase character. In the paired regime, the characteristic response scale acquires a growing fractional sensitivity to the intralayer hopping and an interaction dependence partway towards the $1/U$ law. These results show how a collective excitation can be tracked across a fermion-to-composite-boson crossover while constraining changes in its microscopic drive.
Comments36 Pages, 6 Figs
