Interaction-induced lattices for bound states: Designing flat bands, quantized pumps and higher-order topological insulators for doublons

TL;DR

This paper introduces a framework for creating interaction-induced geometric and topological effects in quantum systems by designing effective lattices for bound states, leading to phenomena like flat bands and topological modes.

Contribution

It presents a novel method to realize interaction-induced topological effects through effective lattice design for doublons, expanding possibilities in quantum engineering.

Findings

Demonstration of flat-band localization due to interactions

Realization of topological pumps driven by interactions

Emergence of higher-order topological corner modes from interactions

Abstract

Bound states of two interacting particles moving on a lattice can exhibit remarkable features that are not captured by the underlying single-particle picture. Inspired by this phenomenon, we introduce a novel framework by which genuine interaction-induced geometric and topological effects can be realized in quantum-engineered systems. Our approach builds on the design of effective lattices for the center-of-mass motion of two-body bound states (\emph{doublons}), which can be created through long-range interactions. This general scenario is illustrated on several examples, where flat-band localization, topological pumps and higher-order topological corner modes emerge from genuine interaction effects. Our results pave the way for the exploration of interaction-induced topological effects in a variety of platforms, ranging from ultracold gases to interacting photonic devices.