Random matrix ensembles defined by a mean-field one-body and chaos generating two-body interaction are proved to describe statistical properties of complex interacting many-body quantum systems in general and complex atomic nuclei (or nuclei in the chaotic region) in particular. These ensembles are generically called embedded ensembles of (1 + 2)-body interactions or simply EE(1 + 2) and their GOE random matrix version is called EGOE(1 + 2). In this paper, we study the distribution of non-overlapping spacing ratios of higher-orders in EGOE(1 + 2) for both fermion and boson systems including spin degree of freedom (also without spin) that have their origin in nuclear shell model and the interacting boson model [V.K.B. Kota, N.D. Chavda, Int. J. Mod. Phys. E 27, 1830001 (2018)]. We obtain a very good correspondence between the numerical results and a recently proposed generalized Wigner surmise like scaling relation. These results confirm that the proposed scaling relation is universal in understanding spacing ratios in complex many-body quantum systems. Using spin ensembles, we demonstrate that the higher order spacing ratio distributions can also reveal quantitative information about the underlying symmetry structure (examples are isospin in lighter nuclei and scissors states in heavy nuclei).

证明了由平均场单体和产生两体相互作用的混沌定义的随机矩阵集合描述了一般相互作用的复杂相互作用多体量子系统的统计性质，特别是复杂原子核（或混沌区域中的核）的统计性质。这些集成体通常称为（1 + 2）-身体相互作用的嵌入式集成体，或简称为EE（1 + 2），而它们的GOE随机矩阵版本称为EGOE（1 + 2）。在本文中，我们研究了费米子和玻色子系统在EGOE（1 + 2）中的高阶非重叠间隔比的分布，包括自旋自由度（也没有自旋），它们的起源都来自核壳模型和相互作用玻色子模型[VKB Kota，ND Chavda，Int。J.莫德 物理 E 27，1830001（2018）]。我们在数值结果和最近提出的广义Wigner假设（如比例关系）之间获得了很好的对应关系。这些结果证实，提出的比例关系在理解复杂多体量子系统中的间距比方面具有普遍性。使用自旋合奏，我们证明了更高阶的间距比分布还可以揭示有关基本对称结构的定量信息（例如，轻核中的同位旋和重核中的剪刀态）。