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Analysis of dynamical properties for the two-site Bose–Hubbard model with an algebraic method

In this work, we propose an algebraic recursion method to study the dynamical evolution of the two-site Bose–Hubbard model. We analyze its properties from the viewpoints of single partite purity, energy, and trace distance, in which the model is considered as a typical bipartite system. The analytical expressions for the quantities are derived. We show that the purity can well reflect the transition between different regimes for the system. In addition, we demonstrate that the transition from the delocalization regime to the self-trapping regime with the ratio η increasing not only happens for an initially local state but also for any initial states. Furthermore, we confirm that the dynamics of the system presents a periodicity for η = 0 and the period is tc = π/2J when the initial state is symmetric.