Entanglement Entropies of the quarter filled Hubbard model

TL;DR

This paper investigates the entanglement entropies in the quarter-filled Hubbard model, revealing size-dependent effects explained by a shell-filling phenomenon and supported by conformal field theory and numerical methods.

Contribution

It introduces a conformal field theory approach to account for size-dependent entanglement entropy contributions in the Hubbard model.

Findings

Entanglement entropies depend on system size mod 8.

Shell-filling effects explain additional entropy contributions.

Numerical results agree with analytic predictions for weak interactions.

Abstract

We study Renyi and von Neumann entanglement entropies in the ground state of the one dimensional quarter-filled Hubbard model with periodic boundary conditions. We show that they 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 show that these can be understood in terms of a "shell-filling" effect, and we develop a conformal field theory approach to calculate the additional contributions to the entropies. These analytic results are found to be in excellent agreement with density matrix renormalisation group computations for weak Hubbard interactions. We argue that for larger interactions the presence of a marginal irrelevant operator in the spin sector strongly affects the entropies at the finite sizes accessible numerically, and we present an effective way to take them into account.