Exact solutions and Dynamical phase transitions in the Lipkin-Meshkov-Glick model with Dual nonlinear interactions

Abstract: Lipkin-Meshkov-Glick (LMG) model is paradigmatic to study quantum phase transition in equilibrium or non-equilibrium systems and entanglement dynamics in a variety of disciplines. The generic LMG model usually incorporates two nonlinear interactions. While the classical dynamics of the single-nonlinear-inteaction LMG model is well understood through Jacobi elliptic functions, the dualinteraction case remains unexplored due to analytical challenges. Here, by constructing an auxiliary function that maps the dynamics to the complex plane of Jacobi elliptic functions, we derive exact solutions of classical dynamics for the dual-interaction LMG model. Based on the exact solutions, we give the classical dynamical phase diagram of the LMG model with dual nonlinear interactions, and find out a non-logarithmic behavior of dynamical criticality which is absent in case of single nonlinear interaction. Our results establish a benchmark to analyze the quantum dynamical phase transitions and many-body entanglement dynamics of finite-size LMG model.