Dynamics of two interacting electrons in a one-dimensional crystal with impurities

TL;DR

This paper explores how electron-electron interactions affect wave packet propagation in a one-dimensional crystal with impurities, using the Hubbard model to analyze dynamical properties and entanglement.

Contribution

It introduces a method to track wave packet evolution and analyzes the impact of interaction strength and initial conditions on electron dynamics and entanglement.

Findings

Interaction influences wave packet spreading and localization.

Initial wave packet extension affects propagation behavior.

Entanglement occurs under specific interaction and initial conditions.

Abstract

We investigated the role that the electron-electron interaction plays on the propagating properties of wave packets in a one-dimensional crystal with impurities. We considered two interacting particles with opposite spins in a band, where we treated their interaction along the Hubbard model. We have obtained the density of states of the crystal for different values of the interaction term, as well as solved the dynamical Schr\"{o}dinger equation by varying the initial conditions. We have introduced a method through which we were able to follow the time evolution of the wave packets for both spins showed in three-dimensional plots, and have evaluated, for each particle, the corresponding $MSD^{\prime}s $ and the centroids as function of time . These measurements allow us to determine the influence of the interaction on dynamical properties. We discussed the combined effect that the extension of the initial wave packets and the interaction strength have on propagating properties. Under certain conditions we obtained an entanglement of the two packets associated with both spins that takes place in a small region of the lattice.