论文标题
开放量子系统中的Krylov复杂性
Krylov Complexity in Open Quantum Systems
论文作者
论文摘要
Krylov的复杂性是对操作员复杂性的一种新颖量度，它表现出普遍的行为并界定了大量其他措施。在这封信中，我们将Krylov的复杂性从封闭的系统概括为耦合到马尔可维亚浴的开放系统，在那里Lindbladian Evolution取代了Hamiltonian Evolution。我们表明，可以将开放系统中的Krylov复杂性映射到半限定链中的非铁质紧密结合模型。我们讨论了非官方术语的属性，并表明，随着Krylov基础指数$ n $的增加，非官方术语的优势线性增加。这样的非高铁紧密结合模型可以表现出确定Krylov复杂性长期行为的局部边缘模式。因此，耗散抑制了Krylov复杂性的生长，长期以来，Krylov的复杂性在有限值的情况下饱和，远小于具有相同Hamitonian的封闭系统的复杂性。我们的结论得到了几个模型的数值结果的支持，例如Sachdev-ye-Kitaev模型和相互作用的费米昂模型。我们的工作提供了讨论开放量子系统的复杂性，混乱和全息图的见解。
Krylov complexity is a novel measure of operator complexity that exhibits universal behavior and bounds a large class of other measures. In this letter, we generalize Krylov complexity from a closed system to an open system coupled to a Markovian bath, where Lindbladian evolution replaces Hamiltonian evolution. We show that Krylov complexity in open systems can be mapped to a non-hermitian tight-binding model in a half-infinite chain. We discuss the properties of the non-hermitian terms and show that the strengths of the non-hermitian terms increase linearly with the increase of the Krylov basis index $n$. Such a non-hermitian tight-binding model can exhibit localized edge modes that determine the long-time behavior of Krylov complexity. Hence, the growth of Krylov complexity is suppressed by dissipation, and at long-time, Krylov complexity saturates at a finite value much smaller than that of a closed system with the same Hamitonian. Our conclusions are supported by numerical results on several models, such as the Sachdev-Ye-Kitaev model and the interacting fermion model. Our work provides insights for discussing complexity, chaos, and holography for open quantum systems.
