Information-theoretic principle of emergent 1-form symmetries

Fuente: arXiv
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Main Authors: Liu, Yu-Jie, Xu, Wen-Tao, Pollmann, Frank, Knap, Michael
Format: Preprint
Published: 2025
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author Liu, Yu-Jie
Xu, Wen-Tao
Pollmann, Frank
Knap, Michael
author_facet Liu, Yu-Jie
Xu, Wen-Tao
Pollmann, Frank
Knap, Michael
contents Higher-form symmetries act on sub-dimensional spatial manifolds of a quantum system. They can emerge as an exact symmetry at low energies even when they are explicitly broken at the microscopic level, making them difficult to characterize. In this work, we propose that the emergence of 1-form symmetries is information-theoretic in nature, precisely characterized by the preservation of information about how quantum states transform under the symmetry. As a consequence, the loss of the emergent 1-form symmetry is an information-theoretic transition which we argue to be revealed from the long-range entanglement in the ensemble of post-measurement states. We analytically determine the regimes in which a 1-form symmetry emerges in product states on one- and two-dimensional lattices. In analytically intractable regimes, we demonstrate how to efficiently detect 1-form symmetries with a global quantum error correction (QEC) decoder and numerically examine the information-theoretic transition of the 1-form symmetry, including systems with $\mathbb{Z}_2$ topological order. As a practical application of our framework, we show that once the 1-form symmetry is detected to exist, a topological quantum phase transition characterized by the spontaneous breaking of the 1-form symmetry can be accurately determined by a disorder parameter. We further argue that our proposed theory for emergent 1-form symmetries offers new perspectives on particle condensation and suggests sharp information-theoretic phase boundaries between Higgs and confining regimes in the $\mathbb{Z}_2$ lattice gauge theory.
format Preprint
id arxiv_https___arxiv_org_abs_2502_17572
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Information-theoretic principle of emergent 1-form symmetries
Liu, Yu-Jie
Xu, Wen-Tao
Pollmann, Frank
Knap, Michael
Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
Higher-form symmetries act on sub-dimensional spatial manifolds of a quantum system. They can emerge as an exact symmetry at low energies even when they are explicitly broken at the microscopic level, making them difficult to characterize. In this work, we propose that the emergence of 1-form symmetries is information-theoretic in nature, precisely characterized by the preservation of information about how quantum states transform under the symmetry. As a consequence, the loss of the emergent 1-form symmetry is an information-theoretic transition which we argue to be revealed from the long-range entanglement in the ensemble of post-measurement states. We analytically determine the regimes in which a 1-form symmetry emerges in product states on one- and two-dimensional lattices. In analytically intractable regimes, we demonstrate how to efficiently detect 1-form symmetries with a global quantum error correction (QEC) decoder and numerically examine the information-theoretic transition of the 1-form symmetry, including systems with $\mathbb{Z}_2$ topological order. As a practical application of our framework, we show that once the 1-form symmetry is detected to exist, a topological quantum phase transition characterized by the spontaneous breaking of the 1-form symmetry can be accurately determined by a disorder parameter. We further argue that our proposed theory for emergent 1-form symmetries offers new perspectives on particle condensation and suggests sharp information-theoretic phase boundaries between Higgs and confining regimes in the $\mathbb{Z}_2$ lattice gauge theory.
title Information-theoretic principle of emergent 1-form symmetries
topic Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
url https://arxiv.org/abs/2502.17572