  We study the distribution of non-overlapping spacing ratios of higher-orders
for complex interacting many-body quantum systems, with and without spin degree
of freedom (in addition to the particle number). The Hamiltonian of such
systems is well represented by embedded one- plus two-body random matrix
ensembles (with and without spin degree of freedom) for fermionic as well as
bosonic systems. 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.
