论文标题
Krylov的复杂性从整合性到混乱
Krylov complexity from integrability to chaos
论文作者
论文摘要
我们应用了一个称为“ Krylov复杂性”的量子复杂性的概念，以研究系统从集成性到混乱的演变。为此，我们研究了可集成的XXZ自旋链，该链充满了整合性破坏变形，使人们可以在可集成和混乱的行为之间进行插值。 K-复合性可以通过其后期饱和值在可集成阶段抑制，并随着系统驱动到混乱阶段而增加，可以充当基础系统的可集成或混乱性质的探测。我们此外，通过将复杂性演变映射到辅助副局部偏离安德森跳跃模型中，将延迟时间结合的（较低）结合到存在的无序数量中。我们将混乱阶段中k复合物的后期饱和度与随机矩阵集合的后期饱和度进行了比较，发现混乱系统确实接近适当的对称类别中的RMT行为。我们研究了结果对K复合性的两种关键要素的依赖性：汉密尔顿的动力学和遵循时间依赖性的操作员的特征。
We apply a notion of quantum complexity, called "Krylov complexity", to study the evolution of systems from integrability to chaos. For this purpose we investigate the integrable XXZ spin chain, enriched with an integrability breaking deformation that allows one to interpolate between integrable and chaotic behavior. K-complexity can act as a probe of the integrable or chaotic nature of the underlying system via its late-time saturation value that is suppressed in the integrable phase and increases as the system is driven to the chaotic phase. We furthermore ascribe the (under-)saturation of the late-time bound to the amount of disorder present in the Lanczos sequence, by mapping the complexity evolution to an auxiliary off-diagonal Anderson hopping model. We compare the late-time saturation of K-complexity in the chaotic phase with that of random matrix ensembles and find that the chaotic system indeed approaches the RMT behavior in the appropriate symmetry class. We investigate the dependence of the results on the two key ingredients of K-complexity: the dynamics of the Hamiltonian and the character of the operator whose time dependence is followed.
