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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Many-body systems

Background:

  • Hilbert-space fragmentation (HSF) is a phenomenon where quantum systems fail to explore their entire state space.
  • Fracton dynamics describes exotic excitations with restricted mobility, leading to anomalous transport.
  • Optical lattice experiments provide a tunable platform for simulating complex quantum models.

Purpose of the Study:

  • To propose and investigate the strongly tilted Bose-Hubbard model as a platform for studying HSF and fracton dynamics in 2D.
  • To explore the quench dynamics and relaxation behavior of the model.
  • To identify and characterize fractonic excitations and their anomalous transport properties.

Main Methods:

  • Perturbative ansatz to identify HSF in the resonant limit.
  • Numerical simulations of quench dynamics to observe state-dependent relaxation.
  • Cellular automaton analysis of fracton dynamics and comparison to hydrodynamic descriptions.

Main Results:

  • Hilbert-space fragmentation is found when the model is tuned to the resonant limit.
  • Relaxation dynamics are strongly dependent on the initial state, a key signature of HSF.
  • Fractonic excitations exhibiting 1D diffusion (z=1/2) and 2D subdiffusion (z=3/4) are identified, showing anomalous transport.

Conclusions:

  • The strongly tilted Bose-Hubbard model is a viable platform for experimental exploration of HSF and fracton physics.
  • The observed state-dependent dynamics and anomalous transport highlight the unique nature of fractonic excitations.
  • The study provides insights into quantum dynamics and transport in fragmented Hilbert spaces.