论文标题
运营商增长的统计机制
A statistical mechanism for operator growth
论文作者
论文摘要
最近有人猜想，在通用量子多体系统中，本地运算符的光谱密度具有最慢的高频衰变，如区域所允许的。我们表明，该“通用操作者生长假设”的无限温度版本适用于$ d \ ge 2 $尺寸的量子液体旋转模型，对于一个维度而言，Chaotic Ising链（带有纵向和横向场）中的量子模型。此外，表现出多体定位的无序混沌伊辛链可以具有与热模型相同的高频光谱密度衰变。我们的论点本质上是统计的，并且基于这样的观察，即光谱密度的矩可以作为保利弦运算符的路径的无标志问题的总和。
It was recently conjectured that in generic quantum many-body systems, the spectral density of local operators has the slowest high-frequency decay as permitted by locality. We show that the infinite-temperature version of this "universal operator growth hypothesis" holds for the quantum Ising spin model in $d \ge 2$ dimensions, and for the chaotic Ising chain (with longitudinal and transverse fields) in one dimension. Moreover, the disordered chaotic Ising chain that exhibits many-body localization can have the same high-frequency spectral density decay as thermalizing models. Our argument is statistical in nature, and is based on the observation that the moments of the spectral density can be written as a sign-problem-free sum over paths of Pauli string operators.
