Entanglement correction due to local interactions in many-body systems

TL;DR

This paper calculates how local interactions modify the entanglement entropy in many-body fermionic systems, showing that the leading scaling remains unchanged while the correction affects the entropy's pre-factor and introduces a sub-leading term.

Contribution

It provides a perturbative calculation of entanglement correction due to local interactions using flow equation holography, extending understanding of entanglement in interacting fermions.

Findings

Leading correction does not alter the entanglement scaling.

Interaction affects the pre-factor of the logarithmic entanglement term.

A sub-leading, size-dependent correction proportional to U^2 is identified.

Abstract

The correction to the area law for the bipartite min-entanglement entropy of weakly and locally interacting fermions is calculated based on a perturbative extension of the flow equation holography method. Explicit calculations for the one- and two-dimensional case (and similarly for higher dimensions) show that the leading correction to the entanglement entropy of non-interacting fermions up to $U^2$ in the interaction strength does not change the scaling, but only affects the pre-factor of the leading logarithmic term multiplying it by the quasiparticle residue. A term sub-leading to the area law is also present. It is proportional to $U^2$ in the interaction strength and scales linearly with the system size.