Anyon condensation and its applications

FJ Burnell - Annual Review of Condensed Matter Physics, 2018 - annualreviews.org
Bose condensation is central to our understanding of quantum phases of matter. Here, we
review Bose condensation in topologically ordered phases (also called topological …

Symmetry fractionalization, defects, and gauging of topological phases

M Barkeshli, P Bonderson, M Cheng, Z Wang - Physical Review B, 2019 - APS
We examine the interplay of symmetry and topological order in 2+ 1-dimensional topological
quantum phases of matter. We present a precise definition of the topological symmetry …

What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetry

SH Shao - arxiv preprint arxiv:2308.00747, 2023 - arxiv.org
We survey recent developments in a novel kind of generalized global symmetry, the non-
invertible symmetry, in diverse spacetime dimensions. We start with several different but …

Fusion category symmetry I: anomaly in-flow and gapped phases

R Thorngren, Y Wang - arxiv preprint arxiv:1912.02817, 2019 - arxiv.org
We study generalized discrete symmetries of quantum field theories in 1+ 1D generated by
topological defect lines with no inverse. In particular, we describe't Hooft anomalies and …

Higher central charges and topological boundaries in 2+ 1-dimensional TQFTs

J Kaidi, Z Komargodski, K Ohmori, S Seifnashri… - SciPost Physics, 2022 - scipost.org
Abstract A 2+ 1-dimensional topological quantum field theory (TQFT) may or may not admit
topological (gapped) boundary conditions. A famous necessary, but not sufficient, condition …

Prediction of toric code topological order from Rydberg blockade

R Verresen, MD Lukin, A Vishwanath - Physical Review X, 2021 - APS
The physical realization of Z 2 topological order as encountered in the paradigmatic toric
code has proven to be an elusive goal. We predict that this phase of matter can be realized …

Symmetric gapped interfaces of SPT and SET states: systematic constructions

J Wang, XG Wen, E Witten - Physical Review X, 2018 - APS
Symmetry-protected topological (SPT) states have boundary't Hooft anomalies that obstruct
the effective boundary theory realized in its own dimension with UV completion and with an …

An invitation to topological orders and category theory

L Kong, ZH Zhang - arxiv preprint arxiv:2205.05565, 2022 - arxiv.org
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 …

Gapped domain walls, gapped boundaries, and topological degeneracy

T Lan, JC Wang, XG Wen - Physical review letters, 2015 - APS
Gapped domain walls, as topological line defects between (2+ 1) D topologically ordered
states, are examined. We provide simple criteria to determine the existence of gapped …

Gauging categorical symmetries in 3d topological orders and bulk reconstruction

M Yu - arxiv preprint arxiv:2111.13697, 2021 - arxiv.org
We use the language of categorical condensation to give a procedure for gauging
nonabelian anyons, which are the manifestations of categorical symmetries in three …