Static and dynamic properties of a one-dimensional spin-1/2 system

We study the static properties and the dynamics of a quantum system described by a one-dimensional spin-1/2 model with nearest neighbor couplings. We analyze the eigenvalues and the eigenstates of this model with different chain sizes and different boundary conditions. From this analysis, we are able to anticipate how fast the excitations should spread over the chain. The more delocalized the eigenstates are, the faster the excitations should move along this chain. Next, we study the evolution of the system numerically and confirm our predictions. All our Mathematica codes are available upon request.