REVIEW 15 cited by
Categorical Landau Paradigm for Gapped Phases
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
Categorical Landau Paradigm for Gapped Phases
read the original abstract
We propose a unified framework to classify gapped infra-red (IR) phases with categorical symmetries, leading to a generalized, categorical Landau paradigm. This is applicable in any dimension and gives a succinct, comprehensive, and computationally powerful approach to classifying gapped symmetric phases. The key tool is the symmetry topological field theory (SymTFT), which is a one dimension higher TFT with two boundaries, which we choose both to be topological. We illustrate the general idea for (1+1)d gapped phases with categorical symmetries and suggest higher-dimensional extensions.
Forward citations
Cited by 15 Pith papers
-
Lattice non-invertible symmetry from non-commuting transfer matrices
For the root-of-unity XXZ chain, non-commuting transfer matrices generate an explicit Onsager algebra and duality defects obeying Z_N Tambara–Yamagami fusion rules.
-
Non-Invertible Anyon Condensation and Level-Rank Dualities
New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
-
Invariants of Sequential Circuits and Generalized Non-Abelian Statistics
Sequential circuit invariants detect non-invertible symmetry anomalies and characterize non-Abelian fermionic loops plus a new mixed topological order in (3+1)D.
-
Twin Phases: Intrinsic Deconfined Quantum Criticality
Twin phases are inequivalent phases sharing a generalized charge under symmetry S, enabling stable direct transitions without spontaneous symmetry breaking even after gauging.
-
Non-Invertible Symmetries on Tensor-Product Hilbert Spaces and Quantum Cellular Automata
Any weakly integral fusion category admits a QCA-refined realization on tensor-product Hilbert spaces with QCA and symmetry indices fixed by the categorical data under defect assumptions.
-
The Line, the Strip and the Duality Defect
Condensation defects in SymTFT descriptions of XY-plaquette and XYZ-cube models realize non-invertible self-duality symmetries at any coupling, with a continuous SO(2) version in the XY-plaquette.
-
SymTFT construction of gapless exotic-foliated dual models
Develops a Mille-feuille SymTFT construction that generates foliated and exotic dual bulk theories realizing gapless boundary models with spontaneous continuous subsystem symmetry breaking, including duals of the XY p...
-
Defect Charges, Gapped Boundary Conditions, and the Symmetry TFT
Defect charges under generalized symmetries correspond one-to-one with gapped boundary conditions of the Symmetry TFT Z(C) on Y = Σ_{d-p+1} × S^{p-1} via dimensional reduction.
-
Lattice Models for Phases and Transitions with Non-Invertible Symmetries
A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
-
$E_\infty^{1,2}$-type Lieb-Schultz-Mattis anomalies, deconfined quantum critical points, and non-invertible symmetry breaking
E∞^{1,2}-type LSM anomalies lead to non-invertible symmetry breaking at type-II deconfined quantum critical points in 1D spin chains.
-
Twin Phases: Intrinsic Deconfined Quantum Criticality
Twin phases share generalized charges under a symmetry, so direct transitions between them are intrinsically beyond-Landau deconfined quantum critical points without hidden symmetry breaking.
-
Categorical Symmetries via Operator Algebras
The symmetry category of a 2D QFT with G-symmetry and anomaly k equals the twisted Hilbert space category Hilb^k(G), whose Drinfeld center is the twisted representation category of the conjugation groupoid C*-algebra,...
-
The Line, the Strip and the Duality Defect
The XY-plaquette model is claimed to possess a continuous SO(2) non-invertible duality symmetry at arbitrary coupling, realized by open condensation defects in its symmetry TFT.
-
Lattice non-invertible symmetry from non-commuting transfer matrices
Constructs lattice realization of Onsager symmetry and ℤ_N Tambara-Yamagami fusion rules in XXZ chain at roots of unity via non-commuting transfer matrices and duality MPO.
-
Les Houches Lecture Notes on Tensor Networks
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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.