Topological bound states in a lattice of rings with nearest-neighbour interactions

TL;DR

This paper investigates topological bound states of ultracold bosons in a lattice of rings, deriving effective models that reveal protected edge states and flat bands under certain conditions.

Contribution

It introduces an effective model for interaction-induced bound states in a lattice of rings, connecting the physical system to topological models like SSH and Creutz ladders.

Findings

System described as a Creutz ladder with orbital angular momentum l=1.

Effective model includes two SSH chains and two Bose-Hubbard chains.

Topologically protected edge states can emerge in the system.

Abstract

We study interaction-induced bound states in a system of ultracold bosons loaded into the states with orbital angular momentum in a one-dimensional staggered lattice of rings. We consider the hard-core limit and strong nearest-neighbour interactions such that two particles in next neighbouring sites are bound. Focusing on the manifold of such bound states, we have derived the corresponding effective model for doublons. With orbital angular momentum $l=1$, the original physical system is described as a Creutz ladder by using the circulations as a synthetic dimension, and the effective model obtained consists of two Su-Schrieffer-Heeger (SSH) chains and two Bose-Hubbard chains. Therefore, the system can exhibit topologically protected edge states. In a structure that alternates $l=1$ and $l=0$ states, the original system can be mapped to a diamond chain. In this case, the effective doublon model corresponds to a Creutz ladder with extra vertical hoppings between legs and can be mapped to two SSH chains if all the couplings in the original system are equal. Tuning spatially the amplitude of the couplings destroys the inversion symmetry of these SSH chains, but enables the appearance of multiple flat bands.