Interacting spinning fermions with quasi-random disorder

TL;DR

This paper rigorously analyzes interacting spinning fermions with quasi-random disorder, revealing how spin influences the persistence of localization and the structure of effective interactions using advanced mathematical techniques.

Contribution

It introduces a novel rigorous RG and KAM approach to study the effects of spin and disorder on fermionic correlations, highlighting differences from spinless cases.

Findings

Localization persists at finite temperature for spinning fermions.

No relevant effective interactions in spinless fermions.

Presence of an additional relevant quartic term in spinning fermions.

Abstract

Interacting spinning fermions with strong quasi-random disorder are analyzed via rigorous Renormalization Group (RG) methods combined with KAM techniques. The correlations are written in terms of an expansion whose convergence follows from number-theoretical properties of the frequency and cancellations due to Pauli principle. A striking difference appears between spinless and spinning fermions; in the first case there are no relevant effective interactions while in presence of spin an additional relevant quartic term is present in the RG flow. The large distance exponential decay of the correlations present in the non interacting case, consequence of the single particle localization, is shown to persist in the spinning case only for temperatures greater than a power of the many body interaction, while in the spinless case this happens up to zero temperature.