Pith. sign in

REVIEW 22 cited by

Models for gapped boundaries and domain walls

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1104.5047 v4 pith:AU4PQJWZ submitted 2011-04-26 cond-mat.str-el math.CTmath.QA

classification cond-mat.str-elmath.CTmath.QA
keywords bulkboundarydomainmodelscalccategoryexcitationsgapped
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk part is constructed using a unitary tensor category $\calC$ as in the Levin-Wen model, whereas the boundary is associated with a module category over $\calC$. We also consider domain walls (or defect lines) between different bulk phases. A domain wall is transparent to bulk excitations if the corresponding unitary tensor categories are Morita equivalent. Defects of higher codimension will also be studied. In summary, we give a dictionary between physical ingredients of lattice models and tensor-categorical notions.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 22 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Discrete quantum systems from topological field theory

    hep-th 2025-06 conditional novelty 8.0 of 10

    A defect-based topological field theory construction yields local gapped lattice Hamiltonians whose ground states reproduce Chern-Simons, toric code, and Levin-Wen models.

  2. Isometric Tensor Network representation of string-net liquids

    cond-mat.str-el 2019-08 conditional novelty 8.0 of 10

    Exact finite-bond-dimension isometric tensor network representations exist for string-net liquid fixed points and for states connected to them by finite-depth local quantum circuits.

  3. Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism

    hep-th 2026-08 conditional novelty 7.0 of 10

    For G=(Z2,Z2,triv,1), the authors classify anomalies via oriented and spin bordism in spacetime dimensions d<=5 and derive the (3+1)D SymTFT boundary conditions, including the equivalence of the anomalous symmetry cat...

  4. Generalized comodule tube algebras for boundary and domain wall defects of (2+1)D topological order

    hep-th 2026-08 conditional novelty 7.0 of 10

    Codimension-2 defects in 2+1D topological order are classified by representations of new comodule tube algebras over the weak Hopf tube algebras of boundary and domain wall excitations.

  5. A Twist on Scattering from Defect Anomalies

    hep-th 2026-05 unverdicted novelty 7.0 of 10

    Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.

  6. Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries

    hep-th 2026-05 unverdicted novelty 7.0 of 10

    Gapped phases dual to massless RG flows in 2D CFTs exhibit unusual ordering via spontaneous breaking of non-group-like symmetries and are characterized using smeared boundary CFTs applied to smeared Ishibashi states.

  7. On the SymTFTs of Finite Non-Abelian Symmetries

    hep-th 2026-03 unverdicted novelty 7.0 of 10

    Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.

  8. Constant-Depth Clifford-Hierarchy Gates via Non-Abelian Surface Codes

    quant-ph 2025-12 conditional novelty 7.0 of 10

    Non-Abelian surface codes based on dihedral groups D_{4N} implement transversal phase gates T^{1/N} at any Clifford-hierarchy level in 2D, with a qubit-only version when 8N is a power of two.

  9. Gauging Non-Invertible Symmetries in (2+1)d Topological Orders

    hep-th 2025-07 conditional novelty 7.0 of 10

    A framework for gauging non-invertible symmetries in (2+1)d TQFTs, unifying 0-form and 1-form gauging via surface algebras, with constraints and toric-code examples.

  10. QG from SymQRG: AdS$_3$/CFT$_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow

    hep-th 2024-12 conditional novelty 7.0 of 10

    A framework called SymQRG identifies 3D quantum gravity as the symmetry-preserving RG flow of 2D CFTs, realized discretely by U_q(SL(2,R)) 6j symbols.

  11. Tube Category, Tensor Renormalization and Topological Holography

    math-ph 2024-12 conditional novelty 7.0 of 10

    For any rigid monoidal category C, the representations of the coend-defined tube category XC are equivalent to the relative center of the Yoneda embedding, with the Drinfeld center Z(C) embedded inside.

  12. Higher Gauging and Non-invertible Condensation Defects

    hep-th 2022-04 unverdicted novelty 7.0 of 10

    Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.

  13. A diagrammatic field theory of quantum error correction

    quant-ph 2026-07 conditional novelty 6.5 of 10

    Exact correctability of fusion-space codes is equivalent to fibrewise Knill–Laflamme conditions on syndrome-admissible footprint algebras, with a conditional Peierls threshold for growing families and explicit Ising e...

  14. A conditional no-go for resource-free magic-axis measurement on a static surface code

    eess.SY 2026-07 conditional novelty 6.0 of 10

    Under three stated assumptions, a resource-free static surface-code patch cannot sharply measure the magic axis at polynomial acceptance; it must pay with a resource, leave the dilute regime, or accept exponentially rarely.

  15. Practical gates by Majorana fermion motion

    quant-ph 2026-06 unverdicted novelty 6.0 of 10

    Majorana fermion motion serves as a primitive for braiding-based logical gates in stabilizer codes, enabling denser packing and numerical outperformance of lattice surgery for 2-qubit Clifford gates under near-term noise.

  16. When Symmetries Twist: Anomaly Inflow on Monodromy Defects

    hep-th 2026-05 unverdicted novelty 6.0 of 10

    Monodromy defects for anomalous symmetries are defined as domain walls between symmetry generators and anomaly-induced topological orders, resulting in protected chiral edge modes and adiabatic pumping of gapless degr...

  17. Higher Representations and Quark Confinement

    hep-th 2025-01 conditional novelty 6.0 of 10

    Using higher-categorical representation theory, the paper proposes that the confined and adjoint Higgs phases of scalar QCD are distinguished by their baryon-charge spectra and by the presence of center vortices.

  18. SymSETs and self-dualities under gauging non-invertible symmetries

    hep-th 2025-01 conditional novelty 6.0 of 10

    A new SymSET-based construction shows that changing symmetry fractionalization classes can change fusion rules of self-duality defects under non-invertible gauging, yielding new fusion categories such as Rep D16 and Rep SD16.

  19. Organizing transitions and their cascades: Generalized symmetry enforcement in massless flows or Higgs transitions

    hep-th 2026-08 conditional novelty 5.0 of 10

    The unbroken fusion ring symmetry FR(SU(2)_{p-2}) stabilizes the massless RG flow M(p,p+1)->M(p-1,p) by making every invariant IR primary field irrelevant.

  20. Operational Tube-Sector Theory of Quantum State Distinguishability Under Generalized Symmetries

    hep-th 2026-06 unverdicted novelty 5.0 of 10

    Introduces tube-sector probabilities from the center of boundary tube algebras to give optimal one-shot distinguishability of quantum states under generalized symmetries.

  21. What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries

    hep-th 2023-08 unverdicted novelty 3.0 of 10

    A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.

  22. Les Houches Lecture Notes on Tensor Networks

    cond-mat.str-el 2025-12 unverdicted novelty 2.0 of 10

    A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.

Pith tools