<p>In this work, we introduce a novel phase field model for simulating polymer crystallization. The model combines the Allen-Cahn equation for interface tracking and the heat equation for temperature evolution. A key feature is its adherence to an energy dissipation law, achieved by coupling the temperature variable to the Allen-Cahn equation via an exponential function and restricting latent heat release to the interface. To the best of our knowledge, this is the first model that guarantees energy dissipation while simulating polymer crystal growth. To solve the model efficiently, we develop two classes of numerical schemes with arbitrary convergence order <i>k</i>. Both schemes are constructed within the generalized scalar auxiliary variable framework with relaxations. The key difference lies in the methods used to update intermediate variables: the first class employs the Runge-Kutta method, while the second class utilizes the exponential time differencing Runge-Kutta method. Both schemes are rigorously proven to be unconditionally energy stable. Finally, extensive numerical experiments are conducted to validate the proposed model and demonstrate the efficiency, accuracy, and unconditional energy stability of the designed schemes.</p>