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arXiv:2508.06272 · Physical Review A

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

Yunjia Zhai, Ayaka Usui, A. M. Marques, R. G. Dias, V. Ahufinger

Published Feb 6, 2026• 0 citations
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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.

DOI
10.1103/7nmy-zflj

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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=1l=1l=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=1l=1l=1 and l=0l=0l=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.
We study the topological properties of interacting and noninteracting bosons loaded in the orbital angular momentum states l=1l=1l=1 in a lattice of rings with alternating distances. At the single-particle level, the two circulation states within each site lead to two decoupled Su-Schrieffer-Heeger lattices with correlated topological phases. We characterize the topological configuration of these lattices in terms of the alternating distances, as well as their single-particle spectrum and topologically protected edge states. Second, we add on-site interactions for the two-boson case, which lead to the appearance of multiple bound states and edge bound states. We investigate the doublon bands in terms of a strong-link model and we analyze the resulting subspaces using perturbation theory in the limit of strong interactions. All analytical results are benchmarked against exact diagonalization simulations.
We study two-particle states in a Su-Schrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with potential walls along specific edges. The 2D SSH model has a trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D) topological invariant, along specific directions of the lattice, which allow for the presence of topological edge states. Using center-of-mass and relative coordinates, we calculate the energy spectrum of these two-body states for strong interactions and find that, aside from the expected appearance of doublon bands, two extra in-gap bands are present. These are identified as bands of topological states localized at the edges of the internal coordinate, the relative distance between the two particles. As such, the topological states reported here are intrinsically many-body in what concerns their real space manifestation, having no counterpart in single-particle states derived from effective models. Finally, we compare the effect of Hubbard interactions with that of NN interactions to show how the presence of the topological bound states is specific to the latter case.
We study a system of a few ultracold bosons loaded into states with orbital angular momentum l=1l=1l=1 of a one-dimensional staggered lattice of rings. Local eigenstates with winding numbers +l+l+l and $\ensuremath{-}l$ form a Creutz ladder with a real dimension and a synthetic one. States with opposite winding numbers in adjacent rings are coupled through complex tunnelings, which can be tuned by modifying the central angle $\ensuremath{\phi}$ of the lattice. We analyze both the single-particle case and the few boson bound-state subspaces for the regime of strong interactions using perturbation theory, showing how the geometry of the system can be engineered to produce an effective $\ensuremath{\pi}$ flux through the plaquettes. We find nontrivial topological band structures and many-body Aharonov-Bohm caging in the NNN-particle subspaces even in the presence of a dispersive single-particle spectrum. Additionally, we study the family of models where the angle $\ensuremath{\phi}$ is introduced at an arbitrary lattice periodicity $\mathrm{\ensuremath{\Gamma}}$. For $\mathrm{\ensuremath{\Gamma}}>2$, the $\ensuremath{\pi}$ flux becomes nonuniform, which enlarges the spatial extent of the Aharonov-Bohm caging as the number of flat bands in the spectrum increases. All the analytical results are benchmarked through exact diagonalization.
Quasi-one-dimensional or ladder models serve as a bridge between one-dimensional and two-dimensional models, providing a simplified framework for incorporating intricate physics. In this study, we extend the concept of the momentum-state lattice by introducing couplings between next-nearest-neighbor sites throughout the entire momentum chain to simulate the staggered Su-Schrieffer-Heeger (SSH) ladder model. This ladder model is a direct extension of the well-known SSH model, recognized as a fundamental progression in modeling systems. Through this model, we explore compelling physical phenomena and successfully replicate the topological phase diagram of the Kitaev-Majorana chain. Utilizing time-averaged mean displacements of wave packets as a metric, we ascertain the topological invariants of the model. By varying staggered dimerization and interchain hopping parameters, we map out the topological phase diagram of the staggered SSH ladder, elucidating the presence of three distinct phases classified by their winding numbers: W = + 1 , 0, and − 1 , respectively.
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, optical lattices and qubits, and provide perspectives for topological two-particle and many-body physics.
We investigate the quantum many-body dynamics of bosonic atoms hopping in a two-leg ladder with strong on-site contact interactions. We observe that when the atoms are prepared in a staggered pattern with pairs of atoms on every other rung, singlon defects, i.e., rungs with only one atom, can localize due to an emergent topological model, even though the underlying model in the absence of interactions admits only topologically trivial states. This emergent topological localization results from the formation of a zero-energy edge mode in an effective lattice formed by two adjacent chains with alternating strong and weak hoping links (Su-Schrieffer-Heeger chains) and opposite staggering which interface at the defect position. Our findings open the opportunity to dynamically generate nontrivial topological behaviors without the need for complex Hamiltonian engineering.