Emergence of Gaussianity in the thermodynamic limit of interacting fermions

TL;DR

This paper investigates how interacting fermion systems become effectively free-fermion-like in the thermodynamic limit, showing that Gaussianity emerges under certain conditions and is experimentally observable.

Contribution

It quantitatively relates system size and correlation length for Gaussianity emergence and demonstrates its robustness to interaction variations and disorder.

Findings

Gaussianity emerges at specific system sizes and correlation lengths

Wick's theorem applicability indicates experimental observability

Emergent Gaussianity is robust to interaction and disorder variations

Abstract

Systems of interacting fermions can give rise to ground states whose correlations become effectively free-fermion-like in the thermodynamic limit, as shown by Baxter for a class of integrable models that include the one-dimensional XYZ spin-$\frac{1}{2}$ chain. Here, we quantitatively analyse this behaviour by establishing the relation between system size and correlation length required for the fermionic Gaussianity to emerge. Importantly, we demonstrate that this behaviour can be observed through the applicability of Wick's theorem and thus it is experimentally accessible. To establish the relevance of our results to possible experimental realisations of XYZ-related models, we demonstrate that the emergent Gaussianity is insensitive to weak variations in the range of interactions, coupling inhomogeneities and local random potentials.