Related Experiment Video
Updated: May 18, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Bound states in the continuum realized in the one-dimensional two-particle Hubbard model with an impurity
J M Zhang1, Daniel Braak, Marcus Kollar
1Theoretical Physics III, Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany.
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.
More Related Videos
Related Concept Videos
Fermi Level
At absolute zero temperature, electrons fill all energy states up to the Fermi level, leaving upper states empty. As the temperature rises,...
Atomic Nuclei: Nuclear Spin State Overview
Types of Semiconductors
Energy Bands in Solids
Band Formation:
When atoms are brought close together, as in a solid, these discrete energy levels begin to split due to the overlap of electron orbitals from adjacent atoms. This split occurs because of the Pauli exclusion principle, which states that no two...
First Law: Particles in One-dimensional Equilibrium
The Entropy as a State Function

