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

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.

💡 Research Summary

The paper addresses a fundamental obstacle to using doublons—bound pairs of bosons occupying the same lattice site—as robust carriers of quantum information in the strongly interacting Bose‑Hubbard model. Even in the limit of large on‑site repulsion (|U|≫J), doublons are not perfectly localized because they can virtually dissociate into two singly‑occupied neighboring sites and recombine, a second‑order process that yields an effective nearest‑neighbor (NN) pair‑hopping amplitude J_eff = 2J²/U. This residual mobility leads to ballistic spreading of doublon wave packets and eventual thermalization, limiting storage times to scales ∝U/J².

To suppress this intrinsic transport without breaking translational symmetry, the authors extend the standard Bose‑Hubbard Hamiltonian by adding an explicit NN pair‑hopping term,  H_p = J_p ∑⟨i,j⟩ p_i† p_j, where p_i = a_i² annihilates a doublon on site i. The direct pair‑hopping amplitude J_p provides a second coherent channel that can interfere destructively with the virtual hopping J_eff. While the naive cancellation condition J_p ≈ –J_eff already reduces transport, higher‑order hybrid processes involving both J and J_p modify the effective amplitude.

The authors perform a systematic third‑order Schrieffer‑Wolff transformation (SWT) to block‑diagonalize the Hamiltonian up to O(J³/U²). They identify two distinct third‑order pathways: (A) a virtual dissociation‑recombination sequence followed by a direct pair hop, and (B) the reverse order. Summing over all nearest‑neighbor intermediates introduces a geometric factor η = 2z, where z is the lattice coordination number. The renormalized effective hopping becomes  J̃_eff = J_p + 2J²/U – η J² J_p/U². Setting J̃_eff = 0 yields the optimal pair‑hopping strength:  J_opt,1D = 2J²/U · (4J² – U²)⁻¹ (z = 2, η = 4),  J_opt,2D = 2J²/U · (8J² – U²)⁻¹ (z = 4, η = 8).

Exact numerical simulations validate these analytical predictions. In a one‑dimensional chain (N = 201, u = |U|/J = 10), a Gaussian doublon wave packet is evolved under three scenarios: (i) no pair hopping (J_p = 0), (ii) heuristic cancellation (J_p = –J_eff), and (iii) the analytically optimal J_p. The RMS displacement shows ballistic growth for case (i), a slowed but still visible light‑cone for case (ii), and near‑complete dynamical arrest for case (iii). Entanglement, quantified by the negativity between symmetric sites, decays orders of magnitude slower under the optimal condition, confirming that the destructive interference protects quantum correlations.

In two dimensions (square lattice), the same optimal J_p reduces the expansion velocity dramatically, yet a residual slow spreading persists due to higher‑order next‑nearest‑neighbor processes that are not canceled by the third‑order condition. The authors note that extending the Hamiltonian with additional terms (e.g., NNN pair hopping) could further suppress these channels.

The many‑body regime is explored by initializing density‑wave states with period‑2 modulation and performing finite‑size scaling (L = 8–16). The density‑wave order remains essentially frozen for times far exceeding the naive doublon hopping time, forming a long‑lived prethermal plateau. This plateau is distinguished from many‑body localization or Hilbert‑space fragmentation because it arises purely from the separation of microscopic (suppressed J̃_eff) and thermalization (exponential in U/J) timescales. The authors demonstrate that the prethermal state retains substantial bipartite entanglement, again highlighting the protective effect of the engineered interference.

Finally, experimental feasibility is discussed. In ultracold‑atom optical lattices, Raman‑assisted processes can realize the required pair‑hopping amplitude with tunable sign and magnitude. In superconducting circuit arrays, nonlinear couplers can generate analogous terms. The geometric factor η depends only on lattice connectivity, making the scheme adaptable to 1D, 2D, and even 3D architectures.

In summary, the work provides a disorder‑free, Hamiltonian‑engineering route to dramatically suppress doublon mobility via destructive quantum interference. By analytically deriving the optimal pair‑hopping condition—including lattice‑geometry corrections—and confirming it with large‑scale numerics, the authors open a pathway toward long‑lived quantum information storage and a deeper understanding of prethermalization in strongly correlated bosonic systems.