Hierarchy of localized many-body bound states in an interacting open lattice

TL;DR

This paper analytically uncovers the formation and hierarchy of boundary-localized many-body bound states in an interacting open lattice, revealing their emergence, continuum binding, and dependence on particle number.

Contribution

It introduces a rigorous analytical framework for understanding boundary-localized states and their hierarchy in interacting open lattices, including recurrence relations for quasi-momentum.

Findings

Boundary-localized bound states emerge with at least three particles.

Localized states can become bound states in continuum under certain conditions.

Hierarchy of many-body bound states predicted for systems with five or more particles.

Abstract

We unveil the mechanism for the formation of puzzled boundary-localized bound states in a spinless fermionic open lattice with nearest-neighbor interactions. By solving the Bethe-ansatz equation analytically, we uncover asymmetrical string solutions corresponding to the boundary-localized bound states, which emerge in systems with at least three particles. The localized bound states can become bound states in continuum in a suitable parameter region. When the number of particles increases to five or more, additional bound states away from the edge are also observed. Through rigorous analysis, we derive recurrence relations of the quasi-momentum of the localized states as a function of the number of particles, predicting the presence of hierarchy of localized many-body bound states in interacting open lattices.