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

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 increases the EE of a typical two-particle excited state above the clean system EE value.