Shell-Filling Effect in the Entanglement Entropies of Spinful Fermions

TL;DR

This paper investigates how shell-filling effects influence entanglement entropies in a one-dimensional quarter-filled Hubbard model, revealing size-dependent anomalies explained through conformal field theory, with implications for higher-dimensional systems.

Contribution

It identifies and explains shell-filling effects in entanglement entropies of spinful fermions, introducing a conformal field theory approach to quantify the extra contributions.

Findings

Entropies depend on system size modulo 8.

Shell-filling effects cause deviations from conformal field theory predictions.

The approach applies to higher dimensions and multicomponent systems.

Abstract

We consider the von Neumann and R\'enyi entropies of the one dimensional quarter-filled Hubbard model. We observe that for periodic boundary conditions the entropies exhibit an unexpected dependence on system size: for L=4 mod 8 the results are in agreement with expectations based on conformal field theory, while for L=0 mod 8 additional contributions arise. We explain this observation in terms of a shell-filling effect, and develop a conformal field theory approach to calculate the extra term in the entropies. Similar shell filling effects in entanglement entropies are expected to be present in higher dimensions and for other multicomponent systems.