Distribution of higher order spacing ratios in one- plus two-body random matrix ensembles with spin symmetry

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).