Pinning of Fermionic Occupation Numbers: General Concepts and One Dimension

TL;DR

This paper investigates the phenomenon of quasipinning of fermionic occupation numbers by generalized Pauli constraints in one-dimensional systems, developing tools to analyze its occurrence and significance across different coupling regimes.

Contribution

It provides a comprehensive study of quasipinning, confirming its presence in larger systems and intermediate couplings, and demonstrates the importance of GPCs beyond Pauli constraints.

Findings

Quasipinning occurs for larger particle numbers and intermediate couplings.

Quasipinning vanishes at very strong couplings.

GPCs are significant beyond the traditional Pauli exclusion principle.

Abstract

Analytical evidence for the physical relevance of generalized Pauli constraints (GPCs) has recently been provided in [PRL 110, 040404]: Natural occupation numbers $\vec{\lambda}\equiv (\lambda_i)$ of the ground state of a model system in the regime of weak couplings $\kappa$ of three spinless fermions in one spatial dimension were found extremely close, in a distance $D_{min}\sim \kappa^8$ to the boundary of the allowed region. We provide a self-contained and complete study of this quasipinning phenomenon. In particular, we develop tools for its systematic exploration and quantification. We confirm that quasipinning in one dimension occurs also for larger particle numbers and extends to intermediate coupling strengths, but vanishes for very strong couplings. We further explore the non-triviality of our findings by comparing quasipinning by GPCs to potential quasipinning by the less restrictive Pauli exclusion principle constraints. This allows us to eventually confirm the significance of GPCs beyond Pauli's exclusion principle.