Onset of random matrix behavior in scrambling systems
Onset of random matrix behavior in scrambling systems
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DOI：
10.1007/jhep07(2018)124
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发表时间：
2018-07-18
影响因子：
5.4
通讯作者：
Tezuka, Masaki
中科院分区：
文献类型：
--
作者：
Gharibyan, Hrant;Hanada, Masanori;Tezuka, Masaki
量子混沌系统的细粒度能谱被广泛认为可以用随机矩阵统计来描述。这种系统的基本尺度是这种行为持续存在的能量范围。我们通过频谱形状因子中的线性增长斜坡区域开始的时间来定义相应的时间尺度。我们称之为流浪汉。本文的目的是研究多体量子系统中的这种尺度，这些系统表现出强烈的混沌，有时被称为置乱系统。我们专注于随机耦合量子比特系统，本地和k-本地（所有对所有的相互作用）和Sachdev-Ye-Kitaev（SYK）模型。使用数值结果，随机量子电路的解析估计，和哈密顿系统的启发式分析，我们发现以下结果。对于具有守恒律的几何局域系统，我们发现tramp由系统的扩散时间决定，对于N个量子比特的一维链，阶数为N-2。这类似于局部单体混沌系统的行为。对于像SYK这样的k-局部系统，时间是log N阶，但是具有与加扰时间不同的前因子和不同的机制。在没有任何守恒定律的情况下，就像在一般的随机量子电路中一样，我们发现流浪汉类似于log N，与连通性无关。
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We de fine the corresponding time scale by the time at which the linearly growing ramp region in the spectral form factor begins. We call this time tramp. The purpose of this paper is to study this scale in many-body quantum systems that display strong chaos, sometimes called scrambling systems. We focus on randomly coupled qubit systems, both local and k-local (all-to-all interactions) and the Sachdev-Ye-Kitaev (SYK) model. Using numerical results, analytic estimates for random quantum circuits, and a heuristic analysis of Hamiltonian systems we find the following results. For geometrically local systems with a conservation law we find tramp is determined by the diffusion time across the system, order N-2 for a 1D chain of N qubits. This is analogous to the behavior found for local one-body chaotic systems. For a k-local system like SYK the time is order log N but with a different prefactor and a different mechanism than the scrambling time. In the absence of any conservation laws, as in a generic random quantum circuit, we find tramp similar to log N, independent of connectivity.