  Interacting spin systems are of fundamental relevance in different areas of
physics, as well as in quantum information science, and biology. These spin
models represent the simplest, yet not fully understood, manifestation of
quantum many-body systems. An important outstanding problem is the efficient
numerical computation of dynamics in large spin systems. Here we propose a new
semiclassical method to study many-body spin dynamics in generic spin lattice
models. The method is based on a discrete Monte Carlo sampling in phase-space
in the framework of the so-called truncated Wigner approximation. Comparisons
with analytical and numerically exact calculations demonstrate the power of the
technique. They show that it correctly reproduces the dynamics of one- and
two-point correlations and spin squeezing at short times, thus capturing
entanglement. Our results open the possibility to study the quantum dynamics
accessible to recent experiments in regimes where other numerical methods are
inapplicable.
