Tamm-Hubbard surface states in the continuum

TL;DR

This paper demonstrates the existence of thresholdless two-particle surface bound states in the continuum within the Bose-Hubbard model, influenced by impurity potential and particle interactions, at the edge of a 1D lattice.

Contribution

It reveals the conditions for Tamm-Hubbard BIC states to exist at the lattice edge, highlighting their thresholdless nature and dependence on impurity potential and particle interactions.

Findings

Surface BIC states can be sustained with infinitesimal impurity potential.

Existence depends on the sign of impurity potential and Hubbard interaction.

States are thresholdless and occur for specific interaction and potential combinations.

Abstract

In the framework of the Bose-Hubbard model, we show that two-particle surface bound states embedded in the continuum (BIC) can be sustained at the edge of a semi-infinite one-dimensional tight-binding lattice for any infinitesimally-small impurity potential $V$ at the lattice boundary. Such thresholdless surface states, that can be referred to as Tamm-Hubbard BIC states, exist provided that the impurity potential $V$ is attractive (repulsive) and the particle-particle Hubbard interaction $U$ is repulsive (attractive), i.e. for $UV<0$.