Exactly solvable dynamics and signatures of integrability in an infinite-range many-body Floquet spin system

We study N qubits having infinite-range Ising interaction and subjected to a periodic pulse of an external magnetic field. We analytically solve the cases of N = 5 to 11 qubits, finding its eigensystem, the dynamics of the entanglement for various initial states, and the unitary evolution operator. These quantities shows signatures of quantum integrability. For the general case of N > 11 qubits, we provide a conjecture on quantum integrability based on the numerical evidence such as degenerate spectrum, and the exact periodic nature of the time-evolved unitary evolution operator and the entanglement dynamics. Using linear entropy, we show that for the class of initial unentangled state, the entanglement periodically displays maximum and zero values.