Floquet Hamiltonian and Entanglement in Spin Systems in Periodic Magnetic Fields

Abstract

We investigate entanglement in a two-spin system with the dipole–dipole interaction in the multi-pulse spin locking nuclear magnetic resonance (NMR) experiment. We discover a conflict between an exact solution and the standard approximation employing a time-independent effective Floquet Hamiltonian. While the exact solution shows nonzero entanglement in the system, the perturbative Floquet approach predicts that entanglement is absent. The failure of the Floquet method is explained by the multivaluedness of the Floquet Hamiltonian. Correct results can only be obtained with a proper choice of the branch of the Hamiltonian. The same issue is present in other applications of the Floquet theorem in the perturbation theory beyond NMR.