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arXiv:2601.20042 · Frontiers of Physics

Correlated dynamics of three-particle bound states induced by emergent impurities in Bose-Hubbard model

Wenduo Zhao, Boning Huang, Yongguan Ke, Chaohong Lee

cond-mat.quant-gasquant-phSubmitted Jan 27, 2026• Announced Jan 29, 2026• 0 citations
v1 · Jan 27, 2026v2 · Apr 27, 2026v3 · May 22, 2026
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Abstract

Bound states, known as particles tied together and moving as a whole, are profound correlated effects induced by particle-particle interactions. While dimer-monomer bound states are manifested as a single particle attached to dimer bound pair, it is still unclear about quantum walks and Bloch oscillations of dimer-monomer bound states. Here, we revisit three-particle bound states in the Bose-Hubbard model and find that interaction-induced impurities adjacent to bound pair and boundaries cause two kinds of bound states: one is dimer-monomer bound state and the other is bound edge states. In quantum walks, the spread velocity of dimer-monomer bound state is determined by the maximal group velocity of their energy band, which is much smaller than that in the single-particle case. In Bloch oscillations, the period of dimer-monomer bound states is one third of that in the single-particle case. Our works provide new insights to the collective dynamics of three-particle bound states.

DOI
10.15302/frontphys.2026.105203

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Bound states, known as particles tied together and moving as a whole, are profound correlated effects induced by particle-particle interactions. While dimer-monomer bound states are manifested as a single particle attached to dimer bound pair, it is still unclear about quantum walks and Bloch oscillations of dimer-monomer bound states. Here, we revisit three-particle bound states in the Bose-Hubbard model and find that interaction-induced impurities adjacent to bound pair and boundaries cause two kinds of bound states: one is dimer-monomer bound state and the other is bound edge states. In quantum walks, the spread velocity of dimer-monomer bound state is determined by the maximal group velocity of their energy band, which is much smaller than that in the single-particle case. In Bloch oscillations, the period of dimer-monomer bound states is one third of that in the single-particle case. Our works provide new insights to the collective dynamics of three-particle bound states.
We pursue three-body bound states in a one-dimensional tight-binding lattice described by the Bose-Hubbard model with strong on-site interaction. Apart from the simple strongly bound ``trimer'' state corresponding to all three particles occupying the same lattice site, we find two novel kinds of weakly bound trimers with energies below and above the continuum of scattering states of a single-particle (``monomer'') and a bound-particle pair (``dimer''). The corresponding binding mechanism can be inferred from an effective Hamiltonian in the strong-coupling regime which contains an exchange interaction between the monomer and the dimer. In the limit of very strong on-site interaction, the exchange-bound trimers attain a universal value of the binding energy. These phenomena can be observed with cold atoms in optical lattices.
Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our recent work on complete characterization of the bound and scattering states of two and three bosonic atoms in a one-dimensional optical lattice. In the case of two atoms, there is a family of interaction-bound "dimer" states of co-localized particles that exists invariantly for either attractive or repulsive on-site interaction, with the energy below or above the two-particle scattering continuum, respectively. Adding then the third particle -- "monomer" -- we find that, apart from the simple strongly-bound "trimer" corresponding to all three particles occupying the same lattice site, there are two peculiar families of weakly-bound trimers with energies below and above the monomer-dimer scattering continuum, the corresponding binding mechanism being an effective particle exchange interaction.
Bound states in the continuum (BICs) are localized modes residing in the radiation continuum. They were first predicted for single-particle states, and became a general feature of many wave systems. In many-body quantum physics, it is still unclear what would be a close analog of BICs, and whether interparticle interaction may induce BICs. Here, we predict a novel type of multiparticle states in the interaction-modulated Bose-Hubbard model that can be associated with the BIC concept. Under periodic boundary conditions, a so-called quasi-BIC appears as a bound pair residing in a standing wave formed by the third particle. Under open boundary conditions, such a hybrid state becomes an eigenstate of the system. We demonstrate that the Thouless pumping of the quasi-BICs can be realized by modulating the onsite interactions in space and time. Surprisingly, while the center of mass of the quasi-BIC is shifted by a unit cell in one cycle, the bound pair moves in the opposite direction with the standing wave.
We study two mobile bosonic impurities immersed in a one-dimensional optical lattice and interacting with a bosonic bath. We employ the exact diagonalization method for small periodic lattices to study stationary properties and dynamics. We consider the branch of repulsive interactions that induce the formation of bound impurities, akin to the bipolaron problem. A comprehensive study of ground-state and low-energy properties is presented, including an examination of the interaction strengths which induce the formation of a bound dimer of impurities. We also study the dynamics induced after an interaction quench to examine the stability of the bound dimers. We reveal that after large interaction quenches from strong to weak interactions the system can show large oscillations over time with revivals of the dimer states. We find that the oscillations are driven by selected eigenstates with phase-separated configurations.
It is well known that an electron in a single-band tight-binding lattice coherently driven by an external dc electric field undergoes Bloch oscillations. In the framework of the extended Hubbard model, here it is shown theoretically that two strongly interacting electrons with on-site and nearest-neighbor site repulsion undergo a sequence of Bloch oscillations and Zener tunneling, the so-called Bloch-Zener oscillations (BZOs), among different narrow bands formed by bound particle states. Such a kind of BZOs arise because of nearest-neighbor site particle interaction and are thus rather distinct than BZOs observed for a single electron in biperiodic lattices supporting two single-particle minibands.
Repulsively bound pairs of particles in a lattice governed by the Bose-Hubbard model can form stable incompressible clusters of dimers corresponding to finite-size n=2n=2n=2 Mott insulators. Here we study the dynamics of hole defects in such clusters corresponding to unpaired particles which can resonantly tunnel out of the cluster into the lattice vacuum. Due to bosonic statistics, the unpaired particles have different effective mass inside and outside the cluster, and ``evaporation'' of hole defects from the cluster boundaries is possible only when their quasimomenta are within a certain transmission range. We show that quasithermalization of hole defects occurs in the presence of catalyzing particle defects which thereby purify the Mott-insulating clusters. We study the dynamics of a one-dimensional system using analytical techniques and numerically exact time-dependent density-matix renormalization-group simulations. We derive an effective strong-interaction model that enables simulations of the system dynamics for much longer times. We also discuss a more general case of two bosonic species which reduces to the fermionic Hubbard model in the strong interaction limit.