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arXiv:2506.13159 · Physical review. B./Physical review. B

Resonant dynamics of one-dimensional dipole-conserving Bose-Hubbard model with time-dependent tensor electric fields

Jiali Zhang, Shaoliang Zhang

Published Mar 20, 2026• 1 citation
arXivHTMLPDF

Abstract

Recently, tensor gauge fields and their coupling to fracton phases of matter have attracted more and more research interest, and a series of novel quantum phenomena arising from the coupling has been predicted. In this article, we propose a theoretical scheme to construct a time-dependent rank-2 tensor electric field by introducing a periodically driving quadratic potential in a dipole-conserving Bose-Hubbard model, and investigate the dynamics of dipole and fracton excitations when the drive frequency is resonant with the on-site interaction. We find that the dynamics are dominated by the splitting of large dipoles with the photon-assisted correlated tunneling and the movement of small dipoles, both of which can be well controlled by the drive amplitude. Our work provides a possible approach for engineering the dynamics of dipole-conserving quantum systems via tensor gauge fields.

DOI
10.1103/5vr6-fswh

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Recently, tensor gauge fields and their coupling to fracton phases of matter have attracted more and more research interest, and a series of novel quantum phenomena arising from the coupling has been predicted. In this article, we propose a theoretical scheme to construct a time-dependent rank-2 tensor electric field by introducing a periodically driving quadratic potential in a dipole-conserving Bose-Hubbard model, and investigate the dynamics of dipole and fracton excitations when the drive frequency is resonant with the on-site interaction. We find that the dynamics are dominated by the splitting of large dipoles with the photon-assisted correlated tunneling and the movement of small dipoles, both of which can be well controlled by the drive amplitude. Our work provides a possible approach for engineering the dynamics of dipole-conserving quantum systems via tensor gauge fields.
Synthetic gauge fields have provided physicists with a unique tool to explore a wide range of fundamentally important phenomena. However, most experiments have focused on synthetic vector gauge fields. The very rich physics brought about by coupling tensor gauge fields to fracton phases of matter remains unexplored in laboratories. Here, we propose schemes to realize synthetic tensor gauge fields that address dipoles instead of single particles. A lattice tilted by a strong linear potential and a weak quadratic potential yields a rank-2 electric field for a dipole formed by a particle-hole pair. Such a rank-2 electric field leads to a new type of Bloch oscillations, which modulates the quadrupole moment and preserves the dipole moment of the system. In higher dimensions, the interplay between interactions and vector gauge potentials imprints a phase to the ring-exchange interaction and thus generates synthetic tensor gauge fields. Such tensor gauge fields make it possible to realize a dipolar Harper-Hofstadter model in laboratories. The resultant dipolar Chern insulators feature chiral edge currents of dipoles in the absence of net charge currents.
We investigate field-induced excitation production from the unit-filled Mott background of a one-dimensional dipole-conserving Bose--Hubbard chain driven by a periodic quadratic potential, realizing a time-dependent rank-two electric field. Unlike protocols that manipulate pre-existing dipolar or fractonic excitations, we address their production from an initially Mott-like state without prepared dipolar or fractonic excitations. A single correlated hop directly nucleates the compact ∣030⟩|030\rangle∣030⟩ configuration at the atomic energy 3U3U3U, while a lower manifold derived from 2U2U2U contains spatially resolved dipole--antidipole configurations. Exact diagonalization shows that finite hopping turns this lower manifold into a dispersive band whose finite-chain edge lies substantially below the compact 3U3U3U scale. Despite this lower energetic edge, its normalized odd-harmonic spectral weight is perturbatively suppressed as (J/U)2(J/U)^2(J/U)2, reflecting virtual hybridization of the initial and final eigenstates. A consistent second-order treatment of the ∣1111⟩↔∣0220⟩|1111\rangle\leftrightarrow|0220\rangle∣1111⟩↔∣0220⟩ channel includes diagonal self-energy shifts and predicts a weak-field resonance displacement confirmed by exact time evolution. Extended-chain dynamics shows genuine dipole--antidipole separation together with redistribution into higher-energy many-body sectors. The resulting mechanism provides a condensed-matter analogue of multiphoton dynamical Schwinger production in which exact dipole conservation replaces mobile opposite charges by mobile opposite dipoles, while isolated fractonic charges remain immobile.
Quantum many-body systems with fractonic excitations can realize fascinating phases of matter. Here, we study the low-energy excitations of a constrained Bose-Hubbard model in one dimension, which conserves the center of mass or, equivalently, the dipole moment in addition to the particle number. This model is known to realize fractonic phases, including a dipole Mott insulator, a dipole Luttinger liquid, and a metastable dipole supersolid. We use tensor network methods to compute spectral functions from the dynamical response of the system and verify predictions from low-energy field theories of the corresponding ground-state phases. We demonstrate the existence of gapped excitations compatible with strong coupling results in a dipole Mott insulator, linear sound modes characteristic of a Luttinger liquid of dipoles, and soft quadratic modes at both zero and finite momenta in a supersolid state with charge density wave order and phase coherence at noninteger filling.
Fractonic constraints can lead to exotic properties of quantum many-body systems. Here, we investigate the dynamics of fracton excitations on top of the ground states of a one-dimensional, dipole-conserving Bose-Hubbard model. We show that nearby fractons undergo a collective motion mediated by exchanging virtual dipole excitations, which provides a powerful dynamical tool to characterize the underlying ground-state phases. We find that, in the gapped Mott insulating phase, fractons are confined to each other as motion requires the exchange of massive dipoles. When crossing the phase transition into a gapless Luttinger liquid of dipoles, fractons deconfine. Their transient deconfinement dynamics scales diffusively and exhibits strong but subleading contributions described by a quantum Lifshitz model. We examine prospects for the experimental realization in tilted Bose-Hubbard chains by numerically simulating the adiabatic state preparation and subsequent time evolution and find clear signatures of the low-energy fracton dynamics.
When particles move through a crystal or optical lattice, their motion can sometimes become frozen by strong external forces -- yet collective motion may still emerge through subtle many-body effects. In this work, we explore such constrained dynamics by realizing a dipole-conserving Bose-Hubbard model, where single atoms are immobile but pairs of particles can move cooperatively while preserving the system's center of mass, i.e. the overall dipole moment of the particle distribution. Starting from a one-dimensional chain of ultracold bosonic atoms in an optical lattice, we generate localized dipole excitations consisting of a hole and a doublon using site-resolved optical potentials and characterize their quantum walks and scattering dynamics. Our study provides a bottom-up investigation of a Hamiltonian with kinetic constraints, and paves the way for exploring low-energy phases of fractonic matter in existing experimental platforms.