PreprintCC BY 4.0arXiv
Long-Range Toric Code: Finite-Temperature Topological Order in Two Dimensions
Abstract
We introduce two-dimensional toric code models with additional long-range loop interactions. Our models preserve the topologically ordered ground states of the ordinary toric code, while confining anyons at zero temperature. For sufficiently long-ranged interactions, we argue that this confinement persists at finite temperatures, strongly constraining anyon mobility and giving rise to finite-temperature topological order. This topological phase acts as a self-correcting quantum memory and exhibits long-range entanglement. For shorter-ranged interactions, signatures of topological order survive only up to an exponentially large length scale at finite temperature, yielding a partially self-correcting quantum memory.
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BibTeX
@misc{gliozzi2026longrange,
title = {{Long-Range Toric Code: Finite-Temperature Topological Order in Two Dimensions}},
author = {Jacopo Gliozzi and Taylor L. Hughes and Kyung-Su Kim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37765},
eprint = {2610.37765},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37765},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Long-Range Toric Code: Finite-Temperature Topological Order in Two Dimensions
AU - Jacopo Gliozzi
AU - Taylor L. Hughes
AU - Kyung-Su Kim
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37765
UR - https://arxiv.org/abs/2610.37765
AB - We introduce two-dimensional toric code models with additional long-range loop interactions. Our models preserve the topologically ordered ground states of the ordinary toric code, while confining anyons at zero temperature. For sufficiently long-ranged interactions, we argue that this confinement persists at finite temperatures, strongly constraining anyon mobility and giving rise to finite-temperature topological order. This topological phase acts as a self-correcting quantum memory and exhibits long-range entanglement. For shorter-ranged interactions, signatures of topological order survive only up to an exponentially large length scale at finite temperature, yielding a partially self-correcting quantum memory.
ER -