For particular fillings, interactions or a periodic potential can lead to phases which break translational symmetry. As a first example, the t-J model for two-leg ladders exhibits commensurate phases at filling n=1/2 and 3/4. We show that the two phases have a different nature by means of the density-matrix renormalization group technique and describe the diamagnetic response of the system at low magnetic flux. A second example is the one of cold atoms loaded in a 1D trap in presence of a lattice plus a superlattice potentials. The competition between interactions and the quasi-periodic potential gives rise to a rich phase diagram. The physical properties of the system can be understood as an intermediate situation between a true random potential and a standard commensurate one.

Aachen