**FM 6-16 . arXiv:1411.0201. **

**Communications in Mathematical
Physics, 342, 1, pp 217-250 (2016)**

**Author** : Vieri
Mastropietro

**Title: Localization
in an interacting quasi-periodic fermionic chain**

**Abstract**:* We consider a many body
fermionic system with an incommensurate external potential and a short range
interaction in one dimension. We prove that, for certain densities and weak
interactions, the zero temperature thermodynamical
correlations are exponentially decaying for large distances, a property
indicating persistence of localization in the interacting ground state. The
analysis is based on Renormalization Group, and convergence of the renormalized
expansion is achieved using fermionic cancellations and controlling the small
divisor problem assuming a Diophantine condition for the frequency.*

**Keywords**: Many body localization