Localization in an interacting quasi-periodic fermionic chain

TL;DR

This paper proves that in a one-dimensional interacting fermionic chain with an incommensurate potential, localization persists at zero temperature under certain conditions, using Renormalization Group techniques.

Contribution

It demonstrates the persistence of localization in an interacting quasi-periodic fermionic system through rigorous Renormalization Group analysis.

Findings

Exponential decay of correlations in the ground state

Localization persists with weak interactions and specific densities

Rigorous proof using fermionic cancellations and Diophantine conditions

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.