Bound States in the Continuum Realized in the One-Dimensional Two-Particle Hubbard Model with an Impurity

TL;DR

This paper discovers a bound state in a one-dimensional two-particle Hubbard model with an impurity, featuring a simple analytical wave function, tunable in and out of the continuum, despite the model's nonintegrability.

Contribution

It introduces a novel bound state with Bethe-ansatz form in a nonintegrable model, with a simple analytical wave function and tunability in the continuum.

Findings

Bound state exists in the continuum band.

Wave function and eigenvalue are analytically simple.

State can be tuned in and out of the continuum.

Abstract

We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.