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arXiv:2311.08455 · Physical Review Letters

Deconfinement Dynamics of Fractons in Tilted Bose-Hubbard Chains

Julian Boesl, Philip Zechmann, Johannes Feldmeier, Michael Knap

Published Apr 2, 2024• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.132.143401

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Bose-Hubbard models are simple paradigmatic lattice models used to study dynamics and phases of quantum bosonic matter. We combine the extended Bose-Hubbard model in the hard-core regime with ring-exchange hoppings. By investigating the symmetries and low-energy properties of the Hamiltonian we argue that the model hosts fractonic defect excitations. We back up our claims with exact numerical simulations of defect dynamics exhibiting mobility constraints. Moreover, we confirm the robustness of our results against fracton symmetry breaking perturbations. Finally, we argue that this model can be experimentally realized in recently proposed quantum simulator platforms with big time crystals, thus paving a way for the controlled study of many-body dynamics with mobility constraints.
We study the entanglement and bipartite fluctuations of fractonic phases in a one-dimensional dipole-conserving Bose-Hubbard chain using the density matrix renormalization group method. We demonstrate that bipartite charge fluctuations fail to detect quantum phase transitions in fractonic systems. Instead, we introduce bipartite dipole fluctuations, Fd{\mathcal{F}}^{d}Fd, which exhibit scaling laws identical to the entanglement entropy SSS. For example, at integer filling n=2n=2n=2, both Fd{\mathcal{F}}^{d}Fd and SSS show logarithmic scaling in dipole Luttinger liquids and area-law scaling in dipole Mott insulators. Interestingly, in the dipole supersolid phase at noninteger filling n=3/2n=3/2n=3/2, we reveal that Fd{\mathcal{F}}^{d}Fd and SSS obey area laws despite the phase being compressible and hosting long-range dipole-dipole order. Moreover, we identify another phase at n=3/2n=3/2n=3/2, previously called the fractional Mott insulator phase, as a dipole-conserving charge density wave state. In this phase, Fd{\mathcal{F}}^{d}Fd and SSS follow area laws, but Fd{\mathcal{F}}^{d}Fd exhibits an additional period-2 oscillation. These findings provide insights into the interplay between dipole conservation, quantum fluctuations, and entanglement in the fractonic phases.
We propose the strongly tilted Bose-Hubbard model as a natural platform to explore Hilbert-space fragmentation (HSF) and fracton dynamics in two dimensions in a setup and regime readily accessible in optical lattice experiments. Using a perturbative ansatz, we find HSF when the model is tuned to the resonant limit of on-site interaction and tilted potential. First, we investigate the quench dynamics of this system and observe numerically that the relaxation dynamics strongly depends on the chosen initial state-one of the key signatures of HSF. Second, we identify fractonic excitations with restricted mobility leading to anomalous transport properties. Specifically, we find excitations that show one-dimensional diffusion (z=1/2) as well as excitations that show subdiffusive behavior in two dimensions (z=3/4). Using a cellular automaton, we analyze their dynamics and compare it to an effective hydrodynamic description.