Many-body quantum chaos in mixtures of multiple species

We study spectral correlations in many-body quantum mixtures of fermions, bosons, and qubits with periodically kicked spreading and mixing of species. We take two types of mixing, namely, Jaynes-Cummings and Rabi, respectively, satisfying and breaking the conservation of a total number of species. We analytically derive the generating Hamiltonians whose spectral properties determine the spectral form factor in the leading order. We further analyze the system-size $(L)$ scaling of Thouless time t*, beyond which the spectral form factor follows the prediction of random matrix theory. The L dependence of t* crosses over from $lnL$ to L² with an increasing Jaynes-Cummings mixing between qubits and fermions or bosons in a finite-size chain, and it finally settles to t*∝O(L²) in the thermodynamic limit for any mixing strength. The Rabi mixing between qubits and fermions leads to t*∝O(lnL), previously predicted for single species of qubits or fermions without total-number conservation.