Doublons, topology and interactions in a one-dimensional lattice

TL;DR

This paper explores the interplay of topology, interactions, and doublon states in a one-dimensional Bose-Hubbard model with Su-Schrieffer-Heeger topology, revealing diverse bound and edge states across different dimerizations.

Contribution

It systematically characterizes the effects of interactions and topology on two-excitation states in a dimerized lattice, including doublons and topological edge states, in a unified framework.

Findings

Identification of scattering and bound bands including doublons.

Discovery of various topological edge states influenced by interactions.

Analysis across different dimerization regimes.

Abstract

We investigate theoretically the Bose-Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called `doublons', when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities and optical lattices, and provide perspectives for topological many-body physics.