A key goal of quantum chaos is to establish a relationship between widelyobserved universal spectral fluctuations of clean quantum systems and randommatrix theory (RMT). For single particle systems with fully chaotic classicalcounterparts, the problem has been partly solved by Berry (1985) within theso-called diagonal approximation of semiclassical periodic-orbit sums.Derivation of the full RMT spectral form factor $K(t)$ from semiclassics hasbeen completed only much later in a tour de force by Mueller et al (2004). Inrecent years, the questions of long-time dynamics at high energies, for whichthe full many-body energy spectrum becomes relevant, are coming at theforefront even for simple many-body quantum systems, such as locallyinteracting spin chains. Such systems display two universal types of behaviourwhich are termed as `many-body localized phase' and `ergodic phase'. In theergodic phase, the spectral fluctuations are excellently described by RMT, evenfor very simple interactions and in the absence of any external source ofdisorder. Here we provide the first theoretical explanation for theseobservations. We compute $K(t)$ explicitly in the leading two orders in $t$ andshow its agreement with RMT for non-integrable, time-reversal invariantmany-body systems without classical counterparts, a generic example of whichare Ising spin 1/2 models in a periodically kicking transverse field.
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机译：量子混沌的一个关键目标是在清洁量子系统的广泛观察到的通用光谱涨落与随机矩阵理论（RMT）之间建立关系。对于具有完全混沌经典对角的单粒子系统，Berry（1985）在半经典周期轨道和的所谓对角线近似中已部分解决了该问题。从半经典中推导了完整RMT频谱形状因子$ K（t）$。穆勒（Mueller）等人（2004）在一次巡回演出中仅完成了很长时间。近年来，即使对于简单的多体量子系统（例如局部相互作用的自旋链），高能的长时间动力学问题（与之相关的整个多体能谱也已成为主流）已经成为最重要的问题。这样的系统表现出两种普遍的行为类型，分别称为“多体局部阶段”和“遍历阶段”。在遍历阶段，即使对于非常简单的相互作用并且在没有任何外部干扰源的情况下，RMT也能很好地描述光谱波动。在这里，我们为这些观测提供了第一个理论解释。我们在$ t $的前两个订单中显式计算$ K（t）$，并显示其与RMT的协议，用于不带经典对等物的不可积分，时间可逆的不变体系统，这是Ising自旋1/2模型的一般示例在周期性踢的横向场中。
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