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

TL;DR

This work addresses the formation and dynamics of three‑particle bound states in the Bose‑Hubbard model under strong interactions ($U\gg J$). By deriving an effective Hamiltonian via second‑order perturbation (Schrieffer–Wolff), the authors reveal two interaction‑induced defects: a boundary defect giving bound edge states and a bulk defect adjacent to a dimer bound pair that hosts dimer–monomer bound states (DMBS). The DMBS exhibit slowed, ballistic quantum walks with a maximal group velocity determined by the DMBS band and Bloch oscillations with a period reduced by a factor of three relative to single particles; edge states localize due to boundary energy offsets. The results illuminate the rich, correlated dynamics of few‑body bound states in lattice systems and point toward potential connections with multi‑particle topological phenomena.

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.

Figures (7)

• Figure 1: Schematics of three particle bound states. The tunneling strength of single particle is $J$, while the bound dimer pair has effective tunneling strength $2J^2/U$ due to particle-particle interaction $U$. (a) Three-particle bound edge state due to interaction-induced defect at the boundaries. (b) dimer-monomer bound state due to interaction-induced defect adjacent to the dimer bound pair.
• Figure 2: Three-particle spectrum and three-particle bound states in the Bose-Hubbard model. (a) Spectrum of the three-particle Bose-Hubbard model. The insets are the enlargement of type-(ii)(iii) regions, and the green and red dots marked the dimer-monomer bound states and type-(iii) bound edge states, respectively. (b1-b3) Second-order correlation functions of three typical dimer-monomer bound states, which are marked by red 'o', 'x', and '+' in inset of (a). (b4) Second-order correlation function of type-(iii) bound edge states. Parameters are set as $J=1$, $U=20$, and $M=30$.
• Figure 3: The validity of the effective model $\hat{H}_{\rm eff}$. (a) Eigenvalues correspond to type-(ii) states given by the original model (blue circles), effective model $H_{\rm{eff}}$ (red dots) and effective model $H_{\rm{eff}}'$ in Ref. PhysRevA.81.011601 (black dots). Insets are the enlargement for parts of the eigenvalues. (b) and (c) are second-order correlation functions of two typical three-particle bound states obtained from the effective Hamiltonian $\hat{H}_{\rm eff}$. Parameters are set as $J=1$, $U=20$, and $M=30$.
• Figure 4: Quantum walks of dimer-monomer bound state. (a) Density distribution as a function of time. (b) Second-order correlation of the evolved state at the end time. The red lines in (a) denotes propagation trajectory predicted by the group velocity. Parameters are set as $J=1$, $U=20$, $M=20$.
• Figure 5: Bloch oscillations of dimer-monomer bound state. (a) Density distribution as a function of time. (b)(c)(d) Second-order correlation functions of the evolved state at three moments marked by red lines in (a), respectively. Parameters are set as $J=1$, $U=20$, $F=0.04$ and $M=20$.