Interference-Induced Suppression of Doublon Transport and Prethermalization in the Extended Bose-Hubbard Model

TL;DR

The paper addresses the intrinsic mobility of doublons in the strongly interacting Bose-Hubbard model and proposes a disorder-free method to suppress transport by adding a nearest-neighbor pair-hopping term that destructively interferes with the dominant second-order hopping channel $J_{ ext{eff}} = 2J^2/U$. Using a third-order Schrieffer-Wolff transformation, it derives an optimal condition $J_p^{\text{opt}} = \frac{2J^2 U}{\eta J^2 - U^2}$ with a geometry-dependent factor $\eta$, yielding exact predictions for 1D ($\eta=4$) and 2D ($\eta=8$). Numerical simulations show near-complete dynamical arrest and entanglement preservation in 1D, and substantial but incomplete suppression in 2D due to residual higher-order pathways; in the many-body regime, a long-lived density-wave plateau arises from a dramatic separation of microscopic and thermalization timescales, indicating prethermalization rather than true localization. The work demonstrates a robust, disorder-free route to Hamiltonian engineering for enhancing quantum information storage, with practical implementation via Floquet engineering in superconducting circuits and avenues for extending control to longer-range hoppings.

Abstract

The coherent mobility of doublons, arising from second-order virtual dissociation-recombination processes, fundamentally limits their use as information carriers in the strongly interacting Bose-Hubbard model. We propose a disorder-free suppression mechanism by introducing an optimized nearest-neighbor pair-hopping term that destructively interferes with the dominant virtual hopping channel. Using the third-order Schrieffer-Wolff transformation, we derive an analytical optimal condition that accounts for lattice geometry corrections. Exact numerical simulations demonstrate that this optimized scheme achieves near-complete dynamical arrest and entanglement preservation in one-dimensional chains, while in two-dimensional square lattices, it significantly suppresses ballistic spreading yet permits a slow residual expansion. Furthermore, in the many-body regime, finite-size scaling analysis identifies the observed long-lived density-wave order as a prethermal plateau emerging from the dramatic separation of microscopic and thermalization timescales.

Figures (6)

• Figure 1: Schematic of doublon dynamics and the suppression mechanism. (a) Second-order tunneling. A doublon tunnels from site $i$ to $j$ via an intermediate state $\ket{\dots, 1_i, 1_j, \dots}$, overcoming the interaction energy gap $\Delta E = U$. This process generates the effective hopping $J_{\text{eff}}$ (blue arrow). (b) Destructive interference. The intrinsic effective amplitude $J_{\text{eff}}$ is canceled by the explicit pair-hopping strength $J_p$ (red arrow) when $J_p \approx -J_{\text{eff}}$. (c) Third-order tunneling. Third-order pathways involving a neighbor $k$. Type A represents virtual processes preceding the pair hop, while Type B shows the converse sequence. Note that $k$ represents all nearest neighbors, including $k=j$ (in Type A) and $k=i$ (in Type B), giving rise to the geometric factor $\eta$.
• Figure 2: Suppression of doublon transport in a 1D-BH chain with $u=10$. The system is initialized in a Gaussian wave packet ($\sigma=5\sqrt{2}$). (a)-(j) Spatiotemporal evolution of site occupation probabilities up to $t=100 \times 2\pi/J_{\text{eff}}$. Columns from left to right display the single-occupancy probability $P_{i,1}$, the double-occupancy component $2P_{i,2}$, and the total particle density $P_{i,1}+2P_{i,2}$. The three rows correspond to different pair-hopping strengths: (a)-(c) No pair hopping ($J_p=0$); (e)-(g) Heuristic cancellation ($J_p = -J_{\text{eff}}$); and (h)-(j) Optimal cancellation ($J_p = J_p^{\text{opt, 1D}}$). The color bars indicate the magnitude of the corresponding quantities. (k)-(l) Time evolution of the RMSD $\sqrt{\braket{\hat{\sigma}^2(t)}}$ for various ratios of $J_p/J_{\text{eff}}$. The color gradient represents the ratio values. The indicated linear growth regimes ($\propto t$) highlight the ballistic nature of the expansion. The inset in (l) plots the final RMSD at $t=100 \times 2\pi/J_{\text{eff}}$ as a function of $J_p/J_{\text{eff}}$, showing a distinct minimum at $\approx -1.042$, consistent with the theoretical optimum derived in Eq. (\ref{['opt1']}).
• Figure 3: Dynamics of the negativity $\mathcal{N}_{-1,1}(t)$ between symmetric sites $i=-1$ and $j=1$. The time axis is plotted on a logarithmic scale. The system is initialized in a Gaussian wave packet ($\sigma=2\sqrt{2}$). The curves compare the decay of entanglement under three conditions. The dashed horizontal line serves as a visual guide to highlight the significantly prolonged preservation of entanglement in the optimal amplitude.
• Figure 4: Suppression of doublon transport in a 2D-BH square lattice. (a) The initial particle density distribution of a Gaussian wave packet at $t=0$ with an initial width $\sqrt{\langle\hat{\sigma}^2\left(0\right)\rangle} = 2.00$. (b)-(d) Snapshots of the density distribution at $t=2\pi/J_{\text{eff}}$ for $J_p=0$, $-J_{\text{eff}}$, and $J_p^{\text{opt, 1D}}$, respectively. The values at the bottom right of each panel indicate the corresponding RMSD. The color bar represents the normalized particle density. (e) Time evolution of the RMSD for the three cases. The vertical dashed line indicates the time $t=2\pi/J_{\text{eff}}$ corresponding to the snapshots (b)-(d).
• Figure 5: Many-body dynamics of a DW state in a 1D-BH chain with $u=10$. The system is initialized in a DW state $|\Psi_0\rangle = |0,2,0,2,\dots,0\rangle$ with $M=6$ doublons on $N=13$ sites. (a)-(c) Spatiotemporal evolution of the local particle density $\langle \hat{n}_i(t) \rangle$ for $J_p=0$, $-J_{\text{eff}}$, and $J_p^{\text{opt, 1D}}$, respectively. (d) Time evolution of the density imbalance $\mathcal{I}(t)$. The red, orange, and blue curves correspond to the cases in (a), (b) and (c), respectively. The inset shows the decay of $\mathcal{I}(t)$ on a logarithmic scale for the controlled cases in (b) and (c). The dashed lines indicate power-law fits $\mathcal{I}(t) \propto t^{-\beta}$, yielding a vanishingly small exponent $\beta \approx 0.01$ for both scenarios (b) and (c).