Hubbard model: Pinning of occupation numbers and role of symmetries

TL;DR

This paper investigates how occupation numbers in the Hubbard model are constrained by generalized Pauli principles, revealing sharp transitions and the influence of symmetries, with implications for ultracold atom experiments.

Contribution

It demonstrates the occurrence of pinning and nonpinning of natural occupation numbers in the Hubbard model and analyzes the role of symmetries and energy crossings in this phenomenon.

Findings

Sharp transitions between pinning and nonpinning states with varying interaction U

Pinning is linked to crossings of occupation numbers or energy levels

Symmetries significantly influence the occurrence of pinning

Abstract

Fermionic natural occupation numbers do not only obey Pauli's exclusion principle, but are even further restricted by so-called generalized Pauli constraints. Such restrictions are particularly relevant whenever they are saturated by given natural occupation numbers $\vec{\lambda}=(\lambda_i)$. For few-site Hubbard models we explore the occurrence of this pinning effect. By varying the on-site interaction $U$ for the fermions we find sharp transitions from pinning of $\vec{\lambda}$ to the boundary of the allowed region to nonpinning. We analyze the origin of this phenomenon which turns out be either a crossing of natural occupation numbers $\lambda_{i}(U), \lambda_{i+1}(U)$ or a crossing of $N$-particle energies. Furthermore, we emphasize the relevance of symmetries for the occurrence of pinning. Based on recent progress in the field of ultracold atoms our findings suggest an experimental set-up for the realization of the pinning effect.