论文标题
在扩展系统及其量子杂质模型中过渡到混乱
Transition to chaos in extended systems and their quantum impurity models
论文作者
论文摘要
混乱为量子信息处理方案设定了一个基本限制。我们研究了与量子光学设备相关的空间扩展量子多体系统中混乱的发作。我们考虑了有限链上的塔维斯 - 卡明斯模型的扩展版本。通过研究水平间距统计数据，相邻的间隙比和光谱形式，我们观察到从集成性到混乱的过渡，因为塔维斯 - 卡明站点之间的跳跃高于有限值。结果是通过精确的数值对角线化获得的，对于扩展的晶格几何形状而言，很难闻名。为了避免这些困难，我们确定了最小的单位量子杂质模型，该模型成功捕获了晶格模型的光谱特性。这种方法旨在适应其他具有较大当地希尔伯特空间的晶格模型。
Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the Tavis-Cummings model on a finite chain. By studying level-spacing statistics, adjacent gap ratios, and spectral form factors, we observe the transition from integrability to chaos as the hopping between the Tavis-Cummings sites is increased above a finite value. The results are obtained by means of exact numerical diagonalization which becomes notoriously hard for extended lattice geometries. In an attempt to circumvent these difficulties, we identify a minimal single-site quantum impurity model that successfully captures the spectral properties of the lattice model. This approach is intended to be adaptable to other lattice models with large local Hilbert spaces.
