Realization of Hilbert Space Fragmentation and Fracton Dynamics in Two 
Dimensions

Will, Melissa; Moessner, Roderich; Pollmann, Frank

doi:10.1103/PhysRevLett.133.196301

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Realization of Hilbert Space Fragmentation and Fracton Dynamics in Two Dimensions

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Moessner, Roderich
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Will, M., Moessner, R., & Pollmann, F. (2024). Realization of Hilbert Space Fragmentation and Fracton Dynamics in Two Dimensions. Physical Review Letters, 133(19): 196301. doi:10.1103/PhysRevLett.133.196301.

Cite as: https://hdl.handle.net/21.11116/0000-0010-504B-0

Abstract

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.