Coupled identical localized fermionic chains with quasi-random disorder

TL;DR

This paper investigates the localization properties of coupled fermionic chains with quasi-random disorder, revealing that localization persists in few chains but may break down in many due to interaction effects and number theoretical properties.

Contribution

It provides a non-perturbative Renormalization Group analysis of localization in multi-chain fermionic systems with quasi-random disorder, highlighting the role of interactions and number theory.

Findings

Localization persists in single and two-chain systems.

For more than two chains, interactions can lead to delocalization.

Number theoretical properties influence the relevance of effective interactions.

Abstract

We analyze the ground state localization properties of an array of identical interacting spinless fermionic chains with quasi-random disorder, using non-perturbative Renormalization Group methods. In the single or two chains case localization persists while for a larger number of chains a different qualitative behavior is generically expected, unless the many body interaction is vanishing. This is due to number theoretical properties of the frequency, similar to the ones assumed in KAM theory, and cancellations due to Pauli principle which in the single or two chains case imply that all the effective interactions are irrelevant; in contrast for a larger number of chains relevant effective interactions are present.