Fractalizing spacetime: Floquet codes with fractonic excitations that are immobile in space and time
Abstract
We generalize fractalization, a procedure for the construction of fracton models, from space to spacetime. We apply spacetime fractalization to construct fracton floquet codes with syndrome excitations that have limited mobility in space and time. This extends the notion of fracton order to intrinsically dynamical quantum phases of matter that are inequivalent to static fracton phases. We find spacetime type-II fracton floquet codes which have no topological excitations that are mobile in space or time. These codes exhibit an extreme form of quantum discrete time crystal order with response periods that scale exponentially in their linear system sizes. In this context, the no-strings rule that characterizes type-II fractons leads to a superlinear scaling of the floquet code fault-distance with time, potentially lowering the time overhead required for quantum error correction.
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BibTeX
@misc{soule2026fractalizing,
title = {{Fractalizing spacetime: Floquet codes with fractonic excitations that are immobile in space and time}},
author = {Juliette Soule and Dominic J. Williamson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03703},
eprint = {2609.03703},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03703},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fractalizing spacetime: Floquet codes with fractonic excitations that are immobile in space and time
AU - Juliette Soule
AU - Dominic J. Williamson
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03703
UR - https://arxiv.org/abs/2609.03703
AB - We generalize fractalization, a procedure for the construction of fracton models, from space to spacetime. We apply spacetime fractalization to construct fracton floquet codes with syndrome excitations that have limited mobility in space and time. This extends the notion of fracton order to intrinsically dynamical quantum phases of matter that are inequivalent to static fracton phases. We find spacetime type-II fracton floquet codes which have no topological excitations that are mobile in space or time. These codes exhibit an extreme form of quantum discrete time crystal order with response periods that scale exponentially in their linear system sizes. In this context, the no-strings rule that characterizes type-II fractons leads to a superlinear scaling of the floquet code fault-distance with time, potentially lowering the time overhead required for quantum error correction.
ER -