模ularity Krylov 复杂度作为面积算子和纠缠岛屿的边界探测器
Modular Krylov Complexity as a Boundary Probe of Area Operator and Entanglement Islands
AI总结：
通过结合AdS/CFT与模ularity Krylov复杂度，研究利用边界动力学重构面积算子并探测黑洞中的岛屿形成与Page转变。
摘要：
我们展示出量子极值表面的面积算子可以直接从边界动力学中重构，而无需参考bulk几何。我们的方法结合了AdS/CFT中的算子代数量子错误纠正（OAQEC）结构与模ularity Krylov复杂度。利用边界模ularity动力学的Lanczos系数，我们提取出限制在纠缠楔代数上的模ularity哈密顿量的谱，并分离出其主贡献，该主贡献被识别为面积算子。该构造是纯粹边界基于的，并且适用于超位置的半经典几何。作为应用，我们利用边界模ularity演化单独诊断岛屿形成和蒸发黑洞的Page转变，而无需任何bulk极值化。更广泛地说，我们的结果确立了模ularity Krylov复杂度作为具体且可计算的探测器，为从边界量子动力学访问黑洞内部提供了一条新途径。
英文摘要：
We show that the area operator of a quantum extremal surface can be reconstructed directly from boundary dynamics without reference to bulk geometry. Our approach combines the operator-algebra quantum error-correction (OAQEC) structure of AdS/CFT with modular Krylov complexity. Using Lanczos coefficients of boundary modular dynamics, we extract the spectrum of the modular Hamiltonian restricted to the algebra of the entanglement wedge and isolate its central contribution, which is identified with the area operator. The construction is purely boundary-based and applies to superpositions of semiclassical geometries as well. As an application, we diagnose island formation and the Page transition in evaporating black holes using boundary modular evolution alone, bypassing any bulk extremization. More broadly, our results establish modular Krylov complexity as a concrete and computable probe of emergent spacetime geometry, providing a new route to accessing black hole interiors from boundary quantum dynamics.
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