High-fidelity patient-specific heart models, or cardiac digital twins, have the potential to revolutionize cardiovascular care by enabling precise diagnosis, personalized treatment planning, and accurate predictions of disease progression. However, the extensive computational cost of these models, particularly in finite element (FE) simulations, remains a significant barrier to their adoption in clinical practice. In this work, we address this challenge by developing a transformer-based data-driven surrogate model to predict left ventricle (LV) dynamics and global hemodynamics. The surrogate model achieves a speed improvement of more than 40,000 times compared to traditional FE simulations while maintaining an acceptable accuracy of 1.44 mm mean absolute error (MAE). In addition, its parallelization capability enables efficient generation of high-volume simulations, making it a compelling replacement for the FE model as a forward simulator in inverse analysis. These advances underscore the potential for the integration of cardiac digital twins into clinical workflows, advancing scalable patient-specific computational modeling in precision cardiology.