Gapless edges of 2d topological orders and enriched monoidal categories

@article{Kong2017GaplessEO,
  title={Gapless edges of 2d topological orders and enriched monoidal categories},
  author={Liang Kong and Hao Zheng},
  journal={Nuclear Physics},
  year={2017},
  volume={927},
  pages={140-165}
}

Figures from this paper

A mathematical theory of gapless edges of 2d topological orders. Part II

This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the possible observables on the 1+1D world sheet of a

A mathematical theory of gapless edges of 2d topological orders. Part I

This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the possible observables on the 1+1D world sheet of a

Topological phase transition on the edge of two-dimensional Z2 topological order

The unified mathematical theory of gapped and gapless edges of 2d topological orders was developed by two of the authors. It provides a powerful tool to study pure edge topological phase transitions

A topological phase transition on the edge of the 2d Z2 topological order

The unified mathematical theory of gapped and gapless edges of 2d topological orders was developed by two of the authors. It provides a powerful tool to study pure edge topological phase transitions

2022 A self-dual boundary phase transition of the 2d Z N topological order

Recently, a unified mathematical theory of the 1d gapped / gapless quantum phase has been developed. In particular, we have a powerful tool to study the topological phase transitions between 1d gapped

Boundary-bulk relation in topological orders

Bulk Entanglement and Boundary Spectra in Gapped Topological Phases

We study the correspondence between boundary spectrum of non-chiral topological orders on an open manifold $\mathcal{M}$ with gapped boundaries and the entanglement spectrum in the bulk of gapped

The boundary phase transitions of the 2+1D $\mathbb{Z}_N$ topological order via topological Wick rotation

In this work, we show that a critical point of a 1d self-dual boundary phase transition between two gapped boundaries of the Z N topological order can be described by a mathematical structure called

Fractional Hall conductivity and spin-c structure in solvable lattice Hamiltonians

The Kapustin-Fidkowski no-go theorem forbids U(1) symmetric topological orders with non-trivial Hall conductivity in (2+1)d from admitting commuting projector Hamiltonians, where the latter is the

Correspondence between bulk entanglement and boundary excitation spectra in two-dimensional gapped topological phases

We study the correspondence between boundary spectrum of non-chiral topological orders on an open manifold $\mathcal{M}$ with gapped boundaries and the entanglement spectrum in the bulk of gapped

References

SHOWING 1-10 OF 101 REFERENCES

Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers

In this paper, we study the relation between topological orders and their gapped boundaries. We propose that the bulk for a given gapped boundary theory is unique. It is actually a consequence of a

Gapped domain walls, gapped boundaries, and topological degeneracy.

By studying many examples, this work finds evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls, including closed 2-manifolds and open 2- manifolds with gapped boundaries.

Boundary-bulk relation in topological orders

Bulk-edge correspondence in (2 + 1)-dimensional Abelian topological phases

The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall states at $\nu=8$ and 12, with

Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory

We study surface operators in 3d Topological Field Theory and their relations with 2d Rational Conformal Field Theory. We show that a surface operator gives rise to a consistent gluing of chiral and

Topological orders and factorization homology

In the study of 2d (the space dimension) topological orders, it is well-known that bulk excitations are classified by unitary modular tensor categories. But these categories only describe the local

Models for Gapped Boundaries and Domain Walls

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

On a q-Analogue of the McKay Correspondence and the ADE Classification of sl̂2 Conformal Field Theories

Abstract The goal of this paper is to give a category theory based definition and classification of “finite subgroups in Uq( s l 2)” where q=eπi/l is a root of unity. We propose a definition of such
...