Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model

• URL: http://arxiv.org/abs/2509.24179v1
• Date: Mon, 29 Sep 2025 01:53:18 GMT
• Title: Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model
• Authors: Zijian Song, Jian-Hao Zhang,
• Abstract summary: Topological orders can be understood as spontaneous symmetry breaking of higher-form symmetries.<n>We extend this framework to mixed states, where symmetries can be either strong or weak.<n>We show that the resulting decohered quantum double mixed states form a locally indistinguishable set, which also constitutes an information convex set.
• Score: 2.839977593898897
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Topological orders can be understood as spontaneous symmetry breaking of higher-form symmetries. In the non-Abelian case, the broken higher-form symmetries are notably non-invertible. In this work, we extend this framework to mixed states, where symmetries can be either strong or weak. In particular, we investigate the strong-to-weak spontaneous symmetry breaking (SWSSB) of non-invertible higher-form symmetries in non-Abelian Kitaev's quantum double models under decoherence. We further show that the resulting decohered quantum double mixed states form a locally indistinguishable set, which also constitutes an information convex set. Importantly, we emphasize that the dimension of this convex set equals the ground-state degeneracy of the corresponding pure state, highlighting that the quantum information encoded in the ground-state subspace is degraded into classical information captured by the convex set of decohered density matrices.

Related papers

• Algebraic Fusion in a (2+1)-dimensional Lattice Model with Generalized Symmetries [0.04077787659104315]
  We develop a framework for deriving the fusion rules of topological defects in higher-dimensional lattice systems with non-invertible generalized symmetries.<n>We explicitly verify that it acts as a partial isometry on the physical Hilbert space, thereby satisfying a recent generalization of Wigner's theorem applicable to non-invertible symmetries.
  arXiv  Detail & Related papers  (2025-12-24T22:01:15Z)
• Anomalies on the Lattice, Homotopy of Quantum Cellular Automata, and a Spectrum of Invertible States [41.99844472131922]
  We develop a rigorous theory of anomalies on the lattice, which are obstructions to gauging global symmetries and the existence of trivial symmetric states.<n>We also construct $$-spectra of a class of invertible states and quantum cellular automata, which allows us to classify both anomalies and symmetry protected topological phases up to blend equivalence.
  arXiv  Detail & Related papers  (2025-12-01T19:00:01Z)
• Obstruction to Ergodicity from Locality and $U(1)$ Higher Symmetries on the Lattice [0.0]
  We argue that the presence of emphany exact $U(1)$ higher-form symmetry, under mild assumptions, presents a fundamental obstruction to ergodicity under unitary dynamics.<n>We show that such systems necessarily exhibit Hilbert space fragmentation and explicitly construct Krylov sectors whose number scales exponentially with system size.
  arXiv  Detail & Related papers  (2025-11-26T19:00:01Z)
• Modulated symmetries from generalized Lieb-Schultz-Mattis anomalies [23.77391435886253]
  We show that spatially modulated symmetries emerge from gauging ordinary symmetries in the presence of generalized LSM type anomalies.<n>Our results provide a unified, nonperturbative framework that ties together LSM constraints and spatially modulated symmetries across dimensions.
  arXiv  Detail & Related papers  (2025-10-21T14:49:19Z)
• Matrix product state classification of 1D multipole symmetry protected topological phases [21.762451041359906]
  We classify one dimensional bosonic symmetry protected topological phases protected respecting multipole symmetries by employing matrix product state formalism.<n>The symmetry action induces projective representations at the ends of an open chain, which we identify via group cohomology.
  arXiv  Detail & Related papers  (2025-09-11T08:26:51Z)
• Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries [20.76275069383104]
  We show that simple quantum spin chains of physical interest are not included in the rigid framework of fusion categories and weak Hopf algebras.<n>We show that our work provides a bridge between well-understood topological defect symmetries and those that arise in more realistic models.
  arXiv  Detail & Related papers  (2025-09-03T18:01:22Z)
• Anomaly-free symmetries with obstructions to gauging and onsiteability [0.35998666903987897]
  We present counterexamples to the lore that symmetries that cannot be gauged or made on-site are necessarily anomalous.<n>Specifically, we construct unitary, internal symmetries of two-dimensional lattice models that cannot be consistently coupled to background or dynamical gauge fields.<n>These symmetries are nevertheless anomaly-free in the sense that they admit symmetric, gapped Hamiltonians with unique, invertible ground states.
  arXiv  Detail & Related papers  (2025-07-28T18:48:39Z)
• SymTFT Approach for Mixed States with Non-Invertible Symmetries [0.0]
  We develop a framework for studying phases of mixed states with strong and weak symmetries.<n>This framework applies not only to group symmetries but also, importantly, to non-invertible symmetries.
  arXiv  Detail & Related papers  (2025-07-07T18:00:02Z)
• Observation of non-Hermitian bulk-boundary correspondence in non-chiral non-unitary quantum dynamics of single photons [31.05848822220465]
  In non-Hermitian systems, preserved chiral symmetry is one of the key ingredients, which plays a pivotal role in determining non-Hermitian topology.<n>We theoretically predict and experimentally demonstrate the bulk-boundary correspondence of a one-dimensional (1D) non-Hermitian system with chiral symmetry breaking.
  arXiv  Detail & Related papers  (2025-04-07T09:43:43Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• Diagnosing Strong-to-Weak Symmetry Breaking via Wightman Correlators [20.572965801171225]
  Recent developments have extended the discussion of symmetry and its breaking to mixed states. We propose the Wightman correlator as an alternative diagnostic tool.
  arXiv  Detail & Related papers  (2024-10-12T02:04:40Z)
• Noninvertible operators in one, two, and three dimensions via gauging spatially modulated symmetry [15.282090777675679]
  We construct concrete lattice models with non-invertible duality defects via gauging spatially modulated symmetries.<n>Our work provides a unified and systematic analytical framework for constructing exotic duality defects by gauging relevant symmetries.
  arXiv  Detail & Related papers  (2024-09-25T08:52:07Z)
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak [4.41737598556146]
  We show that strong symmetry always spontaneously breaks into the corresponding weak symmetry. We conjecture that this relation among strong-to-weak symmetry breaking, gapless modes, and symmetry-charge diffusion is general for continuous symmetries.
  arXiv  Detail & Related papers  (2024-06-27T17:55:36Z)
• Identifying the Group-Theoretic Structure of Machine-Learned Symmetries [41.56233403862961]
  We propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries.
  arXiv  Detail & Related papers  (2023-09-14T17:03:50Z)
• Entanglement-enabled symmetry-breaking orders [0.0]
  A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state.
  arXiv  Detail & Related papers  (2022-07-18T18:00:00Z)
• Stationary State Degeneracy of Open Quantum Systems with Non-Abelian Symmetries [3.423206565777368]
  We study the null space degeneracy of open quantum systems with multiple non-Abelian, strong symmetries. We apply these results within the context of open quantum many-body systems. We find that the derived bound, which scales at least cubically in the system size the $SU(2)$ symmetric cases, is often saturated.
  arXiv  Detail & Related papers  (2019-12-27T15:50:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.