AI 中文总结
该研究提出含辅助量子比特的混合场伊辛链模型，通过调控无量纲参数 λ 实现快速 scrambling 与算符 confinement 的 crossover，揭示相关隐藏对称性，调和了星型几何两种 scrambling 行为的矛盾。
AI 中文摘要
我们展示了一个静态、无 disorder 的自旋链哈密顿量，通过调控与辅助量子比特的耦合，实现了超弹道、辅助加速的 scrambling 与亚弹道算符 confinement 之间的 crossover。我们的最小模型是混合场伊辛链，带有一个与纵向磁化耦合的自旋-1/2 辅助量子比特。当辅助量子比特弱耦合时，它介导有效的全对全相互作用，加速算符扩散和纠缠增长；而当辅助量子比特耦合较强时，它会迅速使纠缠饱和，并将自旋链算符投影到有效冻结的子空间中。我们通过两个独立方式定位该 crossover：一是互信息饱和时间在 λ_c N/h ≈8 附近的发散峰，二是后期 OTOC 增长率的指数抑制，logα ∝1/λ。通过 Feshbach-Fano 投影和 Schrieffer-Wolff 变换，我们揭示了链上的有效隐藏对称性，该对称性将算符 confinement 在与耦合强度成指数关系的时间内。这调和了星型几何随机幺正电路实现中报道的快速 log(N) scrambling，及其时间独立哈密顿量对应物中先前发现的 confinement，表明二者均来自单一哈密顿量族，且作为一个无量纲参数的函数出现。
英文摘要
We demonstrate a static, disorder-free spin chain Hamiltonian which, by tuning the coupling to an auxiliary qubit, realizes a crossover between super-ballistic, ancilla-accelerated scrambling and sub-ballistic operator confinement. Our minimal model is the mixed-field Ising chain with a spin-1/2 ancilla coupled to its longitudinal magnetization. The ancilla mediates an effective all-to-all interaction which accelerates operator spreading and entanglement growth when weakly coupled, but rapidly saturates its entanglement and projects spin chain operators into effectively frozen subspaces when the ancilla coupling is strong. We locate this crossover independently through both a divergent peak in the mutual-information saturation time near $λ_c N/h \approx 8$ and an exponential suppression of the late-time OTOC growth rate, $\logα\propto 1/λ$. Through a Feshbach-Fano projection and Schrieffer-Wolff transformation, we reveal an effective hidden symmetry on the chain which confines operators on the chain for a time exponential in the coupling strength. This reconciles the fast, $\log(N)$ scrambling reported for random-unitary-circuit realizations of the star geometry with the confinement previously found in its time-independent Hamiltonian analog, showing both emerge from a single Hamiltonian family as a function of one dimensionless parameter.
Comments19 page, 9 figures
