Interacting fermions with quasi-random disorder

We discuss the effect of many-body interactions in fermionic systems with strong quasi-random disorder (quasi-periodic potential). By assuming Diophantine conditions on the frequency and density and using renormalization-group methods, we prove the convergence of the expansion of the many-body correlations up to zero temperature and their exponential decay. This is true, in particular, for the interacting spinless fermionic Aubry-Andre model, for two coupled chains of spinless interacting disordered fermions, and for an array of noninteracting chains with the same disorder in all the chains. Zero-temperature exponential decay is a signal of persistence of localization in the many-body ground state in presence of an interaction. In other systems, however, as in the presence of spin or when more than two interacting chains are coupled, additional relevant processes prevent convergence up to zero temperature, suggesting a lack of localization at least for certain quantities. This is in agreement with recent experiments performed on cold atoms and with numerical simulations.