My research activity is focused on the theoretical understanding of the role played by strong interactions in low-dimensional quantum many-body systems, such as spin chains or Hubbard-like models. In this context I am investigating some peculiar aspects of quantum matter (including phase transitions, magnetism, and non-equilibrium dynamics), which can be experimentally accessed by means of quantum simulators. Among the available platforms, I am dealing with cold atoms trapped in optical lattices and with coupled-cavity quantum electrodynamics (QED). I work on numerical methods for strongly correlated systems, in particular the density matrix renormalization group (DMRG) and tensor networks.