Two particle excited states entanglement entropy in a one-dimensional ring

TL;DR

This paper analyzes the entanglement entropy of two-particle excited states in a one-dimensional ring, revealing how disorder and interactions influence EE, with analytical and numerical results showing the effects on EE in various regimes.

Contribution

It provides an analytical expression for EE in clean systems and numerical insights into how disorder and interactions affect EE in two-particle states.

Findings

EE is twice the single-particle EE when momenta differ significantly.

Disorder reduces the median EE of two-particle states.

Interactions mitigate EE decrease and can increase EE near the localization length.

Abstract

The properties of the entanglement entropy (EE) of two particle excited states in a one-dimensional ring are studied. For a clean system we show analytically that as long as the momenta of the two particles are not close, the EE is twice the value of the EE of any single particle state. For almost identical momenta the EE is lower than this value. The introduction of disorder is numerically shown to lead to a decrease in the median EE of a two particle excited state, while interactions (which have no effect for the clean case) mitigate the decrease. For a ring which is of the same size as the localization length, interaction increase the EE of a typical two particle excited state above the clean system EE value.