The phase screen method is a well-established approach to take into account the effects of atmospheric turbulence in astronomical seeing. This is of key importance in designing adaptive optics for new-generation telescopes, in particular in view of applications such as exoplanet detection or long-exposure spectroscopy. We present an innovative approach to simulate turbulent phase that is based on stochastic realization theory. The method shows appealing properties in terms of both accuracy in reconstructing the structure function and compactness of the representation.