We present results on the localization properties of ground-states of quantum many-body models in a given configuration basis. I will first introduce measures of this localization by defining the corresponding Shannon and Renyi entropies. I will review recent exact results obtained in the literature for spin chains, where sub-leading terms in the scaling of these entropies are found to take an intriguing universal behaviour. I will then present schemes to measure these localization entropies with Quantum Monte Carlo simulations, and will finally show results for 1d and 2d quantum spin systems. Work done in collaboration with Nicolas Laflorencie and David Luitz

Laboratoire de Physique Théorique, Univ. P. Sabatier, Toulouse.