Fermionic bound states on a one-dimensional lattice

TL;DR

This paper investigates the formation and characteristics of bound states of two fermions in a one-dimensional extended Hubbard model, revealing three distinct types with unique properties and localization behaviors.

Contribution

It identifies and characterizes three different types of fermionic bound states in a 1D lattice, including their symmetry and localization properties, expanding understanding of fermion interactions.

Findings

Three types of bound states identified: U, V symmetric, and V antisymmetric.

V-states exhibit diverging localization length below a critical wave number.

All bound states become compact at the Brillouin zone edge.

Abstract

We study bound states of two fermions with opposite spins in an extended Hubbard chain. The particles interact when located both on a site or on adjacent sites. We find three different types of bound states. Type U is predominantly formed of basis states with both fermions on the same site, while two states of type V originate from both fermions occupying neighbouring sites. Type U, and one of the states from type V, are symmetric with respect to spin flips. The remaining one from type V is antisymmetric. V-states are characterized by a diverging localization length below some critical wave number. All bound states become compact for wave numbers at the edge of the Brilloin zone.