Pair formation in two electron correlated chains

TL;DR

This paper investigates how two correlated electrons behave in a tight-binding chain with on-site and nearest neighbor interactions, revealing bound states and their conditions for low-temperature filling.

Contribution

It introduces a detailed analysis of bound states of two electrons with various spin configurations in a correlated chain, including conditions for their formation.

Findings

Electrons form bound states with exponential decay in amplitude.

Correlated bands can have positive or negative energy depending on interaction type.

Conditions for filling these states at low temperatures are discussed.

Abstract

We study two correlated electrons in a nearest neighbour tight- binding chain, with both on site and nearest neighbour interaction. Both the cases of parallel and antiparallel spins are considered. In addition to the free electron band for two electrons, there are correlated bands with positive or negative energy, depending on wheather the interaction parameters are repulsive or attractive. Electrons form bound states, with amplitudes that decay exponentially with separation. Conditions for such states to be filled at low temperatures are discussed.