We study the one-dimensional Bose-Hubbard model under the resonant condition, where the nearest-neighbor and on-site interaction strengths are equal. In the strong interaction limit, $n$ bosons occupied in a single site can transfer to neighboring sites in a complete manner, which is referred to as quantum slinky motion. It can be shown that quantum slinky motions can be described by a set of effective noninteracting Hamiltonians. These Hamiltonians are sets of generalized Su-Schrieffer-Heeger chains with an $n$ -site unit cell in an auxiliary space, referred to as trimerization, tetramerization, pentamerization, etc., possessing nontrivial Zak phases. The corresponding edge states are demonstrated by the $n$ -boson bound states at the ends of the chains. We also investigate the dynamic detection of edge boson clusters through an analysis of quench dynamics. Numerical results indicate that stable edge oscillations clearly manifest the interaction-induced topological features within the extended Bose-Hubbard model.We study the one-dimensional Bose-Hubbard model under the resonant condition, where the nearest-neighbor and on-site interaction strengths are equal. In the strong interaction limit, $n$ bosons occupied in a single site can transfer to neighboring sites in a complete manner, which is referred to as quantum slinky motion. It can be shown that quantum slinky motions can be described by a set of effective noninteracting Hamiltonians. These Hamiltonians are sets of generalized Su-Schrieffer-Heeger chains with an $n$-site unit cell in an auxiliary space, referred to as trimerization, tetramerization, pentamerization, etc., possessing nontrivial Zak phases. The corresponding edge states are demonstrated by the $n$-boson bound states at the ends of the chains. We also investigate the dynamic detection of edge boson clusters through an analysis of quench dynamics. Numerical results indicate that stable edge oscillations clearly manifest the interaction-induced topological features within the extended Bose-Hubbard model.

arXiv:2410.13252Physical review. B./Physical review. BJun 2, 20251 citation

Topological bound states in interacting Su–Schrieffer–Heeger rings

A M Marques, R G Dias

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 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.

arXiv:1710.09148Journal of Physics Condensed MatterJun 19, 201838 citations

Ground-State of the Bose-Hubbard Model

Jay D. Mancini, Vassilios Fessatidis, S.P. Bowen +2 more

Bulletin of the American Physical SocietyMar 17, 20160 citations

The one-dimensional extended Bose-Hubbard model

Ramesh V. Pai, Rahul Anil Pandit

Journal of Chemical SciencesOct 1, 20030 citations

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

Yunjia Zhai, Ayaka Usui, A. M. Marques +2 more

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.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.

arXiv:2508.06272Physical Review AFeb 6, 20260 citations

We study the one-dimensional Bose-Hubbard model under the resonant condition, where the nearest-neighbor and on-site interaction strengths are equal. In the strong interaction limit,

n

bosons occupied in a single site can transfer to neighboring sites in a complete manner, which is referred to as quantum slinky motion. It can be shown that quantum slinky motions can be described by a set of effective noninteracting Hamiltonians. These Hamiltonians are sets of generalized Su-Schrieffer-Heeger chains with an

n

-site unit cell in an auxiliary space, referred to as trimerization, tetramerization, pentamerization, etc., possessing nontrivial Zak phases. The corresponding edge states are demonstrated by the

n

-boson bound states at the ends of the chains. We also investigate the dynamic detection of edge boson clusters through an analysis of quench dynamics. Numerical results indicate that stable edge oscillations clearly manifest the interaction-induced topological features within the extended Bose-Hubbard model.

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.