论文标题
数值探测通用操作员生长假设
Numerically Probing the Universal Operator Growth Hypothesis
论文作者
论文摘要
最近，提出了关于单位不断发展的操作员的复杂性增长的假设。该假设指出，在通用的，不可融合的多体系统中，所谓的兰开斯系数与自相关函数相关的是渐近线性的，并在一维系统中具有对数校正。相比之下，在可集成或自由模型中预计增长将较慢。在手头的论文中，我们对各种示例性系统（包括1D和2D ISING模型以及1D海森贝格模型）进行数值检验。尽管我们发现对所有考虑的ISING模型实际上实现了假设，但在Heisenberg模型的可达到的数值数据中无法观察到假设的普遍行为的开始。提出的对操作员生长的线性结合最终源于涉及哈密顿量和晶格配置的几何参数。我们研究了这样的几何结合，发现任何被考虑的模型都无法实现它。
Recently, a hypothesis on the complexity growth of unitarily evolving operators was presented. This hypothesis states that in generic, non-integrable many-body systems the so-called Lanczos coefficients associated with an autocorrelation function grow asymptotically linear, with a logarithmic correction in one-dimensional systems. In contrast, the growth is expected to be slower in integrable or free models. In the paper at hand, we numerically test this hypothesis for a variety of exemplary systems, including 1d and 2d Ising models as well as 1d Heisenberg models. While we find the hypothesis to be practically fulfilled for all considered Ising models, the onset of the hypothesized universal behavior could not be observed in the attainable numerical data for the Heisenberg model. The proposed linear bound on operator growth eventually stems from geometric arguments involving the locality of the Hamiltonian as well as the lattice configuration. We investigate such a geometric bound and find that it is not sharply achieved for any considered model.
