Two-particle states in the Hubbard model

TL;DR

This paper analytically characterizes two-particle states in the 1D Hubbard model, distinguishing between free scattering states and bound dimers, enhancing understanding of particle interactions in lattice systems.

Contribution

It provides explicit analytic expressions for two-particle states, clarifying their classification and properties in the Hubbard model with attractive or repulsive interactions.

Findings

Explicit formulas for two-particle states

Classification into scattering and bound states

Framework for understanding particle interactions

Abstract

We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle states, which can be classified as (i) scattering states of asymptotically free particles and (ii) interaction-bound dimer states. Our results provide a very transparent framework to understand the properties of interacting pairs of particles in a lattice.