Aspects of entanglement in non-local field theories with fractional Laplacian

TL;DR

This paper investigates how long-range interactions modeled by a fractional Laplacian affect entanglement properties, showing slower decay and absence of revivals in long-range systems compared to short-range models.

Contribution

It provides the first detailed analysis of entanglement dynamics in non-local models with fractional Laplacians, highlighting unique long-range effects.

Findings

Logarithmic negativity decays slower with distance in long-range models.

No revivals of entanglement observed after quantum quenches in long-range systems.

Entanglement entropy supports the distinct behavior of long-range interactions.

Abstract

In recent years, various aspects of theoretical models with long range interactions have attracted attention, ranging from out-of-time-ordered correlators to entanglement. In the present paper, entanglement properties of a simple non-local model with long-range interactions in the form of a fractional Laplacian is investigated in both static and a quantum quench scenario. Logarithmic negativity, which is a measure for entanglement in mixed states is calculated numerically. In the static case, it is shown that the presence of long-range interaction ensures that logarithmic negativity decays much slower with distance compared to short-range models. For a sudden quantum quench, the temporal evolution of the logarithmic negativity reveals that, in contrast to short-range models, logarithmic negativity exhibits no revivals for long-range interactions for the time intervals considered. To further support this result, a simpler measure of entanglement, namely the entanglement entropy is also studied for this class of models.