Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, CNRS, F-95302 Cergy-Pontoise, France.
Phys Rev Lett. 2023 Apr 7;130(14):140403. doi: 10.1103/PhysRevLett.130.140403.
We show that non-Hermitian Ginibre random matrix behaviors emerge in spatially extended many-body quantum chaotic systems in the space direction, just as Hermitian random matrix behaviors emerge in chaotic systems in the time direction. Starting with translational invariant models, which can be associated with dual transfer matrices with complex-valued spectra, we show that the linear ramp of the spectral form factor necessitates that the dual spectra have nontrivial correlations, which in fact fall under the universality class of the Ginibre ensemble, demonstrated by computing the level spacing distribution and the dissipative spectral form factor. As a result of this connection, the exact spectral form factor for the Ginibre ensemble can be used to universally describe the spectral form factor for translational invariant many-body quantum chaotic systems in the scaling limit where t and L are large, while the ratio between L and L_{Th}, the many-body Thouless length is fixed. With appropriate variations of Ginibre models, we analytically demonstrate that our claim generalizes to models without translational invariance as well. The emergence of the Ginibre ensemble is a genuine consequence of the strongly interacting and spatially extended nature of the quantum chaotic systems we consider, unlike the traditional emergence of Hermitian random matrix ensembles.
我们表明，非厄米 Ginibre 随机矩阵行为出现在空间方向上的扩展多体量子混沌系统中，就像厄米随机矩阵行为出现在时间方向上的混沌系统中一样。从平移不变模型开始，这些模型可以与具有复谱的对偶转移矩阵相关联，我们表明，谱形因子的线性斜坡要求对偶谱具有非平凡的相关性，实际上属于 Ginibre 系综的普遍性类别，通过计算能级间距分布和耗散谱形因子来证明。由于这种联系，Ginibre 系综的确切谱形因子可以用于普遍描述在大的 t 和 L 标度极限下平移不变的多体量子混沌系统的谱形因子，而 L 与 L_{Th}（多体 Thouless 长度）的比值是固定的。通过 Ginibre 模型的适当变化，我们分析证明了我们的主张也适用于没有平移不变性的模型。与传统的厄米随机矩阵系综的出现不同，Ginibre 系综的出现是我们所考虑的强相互作用和空间扩展的量子混沌系统的真正结果。
