## 21 Citations

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

- Physics, Mathematics
- 2021

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

- Physics, MathematicsJournal of High Energy Physics
- 2020

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

- Mathematics
- 2020

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

- Mathematics
- 2019

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

- Mathematics, Physics
- 2022

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…

### Bulk Entanglement and Boundary Spectra in Gapped Topological Phases

- Mathematics
- 2018

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

- Mathematics
- 2022

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

- MathematicsJournal of High Energy Physics
- 2023

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

- PhysicsPhysical Review B
- 2019

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

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- Mathematics
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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.

- Mathematics, PhysicsPhysical review letters
- 2015

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.

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

- Physics
- 2014

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

- Mathematics
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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…

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- Mathematics
- 2016

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

- Mathematics
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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…

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- Physics
- 1993

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

- Mathematics
- 2002

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…