Interaction induced doublons and embedded topological subspace in a complete flat-band system

TL;DR

This paper explores how weak interactions induce doublons with unique dynamics and topological properties in a flat-band bosonic system, revealing embedded topological subspaces and edge modes.

Contribution

It introduces an effective Hamiltonian approach showing doublons as quasi-particles and uncovers an interaction-induced topological subspace with edge modes.

Findings

Doublons behave as well-defined quasi-particles with itinerant behavior.

An embedded topological subspace with a bulk invariant is identified.

Interaction-induced topological edge modes are predicted in open systems.

Abstract

In this work, we investigate effects of weak interactions on a bosonic complete flat-band system. By employing a band projection method, the flat-band Hamiltonian with weak interactions is mapped to an effective Hamiltonian. The effective Hamiltonian indicates that doublons behave as well-defined quasi-particles, which acquire itinerancy through the hopping induced by interactions. When we focus on a two-particle system, from the effective Hamiltonian, an effective subspace spanned only by doublon bases emerges. The effective subspace induces spreading of a single doublon and we find an interesting property: The dynamics of a single doublon keeps short-range density-density correlation in sharp contrast to a conventional two-particle spreading. Furthermore, when introducing a modulated weak interaction, we find an interaction induced topological subspace embedded in the full Hilbert space. We elucidate the embedded topological subspace by observing the dynamics of a single doublon, and show that the embedded topological subspace possesses a bulk topological invariant. We further expect that for the system with open boundary the embedded topological subspace has an interaction induced topological edge mode described by the doublon. The bulk--edge--correspondence holds even for the embedded topological subspace.