REVIEW 8 cited by
An invitation to topological orders and category theory
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
read the original abstract
Although it has been a well-known fact, for more than two decades, that category theory is needed for the study of topological orders, it is still a non-trivial challenge for students and working physicists to master the abstract language of category theory. In this work, for those who have no background in category theory, we explain in great details how the structure of a (braided) fusion category naturally emerges from lattice models and physical intuitions. Moreover, we show that nearly all mathematical notions and constructions in fusion categories and its representation theory, such as (monoidal) functors, Drinfeld center, module categories, Morita equivalence, condensation completion and fusion 2-categories, naturally emerge from lattice models and physical intuitions. In this process, we also introduce some basic notions and important results of topological orders.
Forward citations
Cited by 8 Pith papers
-
On $R$-parastatistics I: Foundation
R-paraparticles, a class of statistics beyond fermions and bosons, are given a complete local-observable theory — pair creation, defect probes of hidden indices, and Hopf-algebra hidden symmetries — plus a classificat...
-
Hypergroup Symmetry in Relative Quantum Field Theories and Chiral Algebras
Framework for hypergroup symmetries in relative QFTs establishes one-to-one correspondence between finite symmetries and finite-index conformal embeddings in rational chiral algebras, with implications for gluing left...
-
Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling
An anyonic Hubbard model on a ladder at half-filling shows a metal-to-charge-density-wave transition and an effective strong-coupling model with four phases, including a Z2 phase and an incommensurate phase.
-
Anyon Condensation In Symmetry-Enriched Topological Phases: $G$-Grading of Multifusion Categories
G-preserving anyon condensation in SET string-net models is equivalent to a compatible N-grading of the input multifusion category, which constructs the child SET input and works even with symmetry fractionalization.
-
$E_\infty^{1,2}$-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.
-
Extending fusion rules with finite subgroups: A general construction of $Z_{N}$ extended conformal field theories and their orbifoldings
Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
-
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.
-
ICTP Lectures on (Non-)Invertible Generalized Symmetries
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.
Discussion (0). Sign in to comment.