Lecture notes on generalized symmetries and applications
In this lecture note, we give a basic introduction to the rapidly developing concepts of
generalized symmetries, from the perspectives of both high energy physics and condensed …
generalized symmetries, from the perspectives of both high energy physics and condensed …
SymTh for non-finite symmetries
F Apruzzi, F Bedogna, N Dondi - arXiv preprint arXiv:2402.14813, 2024 - arxiv.org
Symmetry topological field theory (SymTFT) is a very convenient tool to study finite
generalized symmetries of a given quantum field theory (QFT). In particular, SymTFTs …
generalized symmetries of a given quantum field theory (QFT). In particular, SymTFTs …
Classification of subsystem symmetry-protected topological phases
We consider symmetry-protected topological (SPT) phases in two dimensions protected by
linear subsystem symmetries, ie, those that act along rigid lines. There is a distinction …
linear subsystem symmetries, ie, those that act along rigid lines. There is a distinction …
Classification of topological phases with finite internal symmetries in all dimensions
A bstract We develop a mathematical theory of symmetry protected trivial (SPT) orders and
anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different …
anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different …
ICTP lectures on (non-) invertible generalized symmetries
S Schäfer-Nameki - Physics Reports, 2024 - Elsevier
What comprises a global symmetry of a Quantum Field Theory (QFT) has been vastly
expanded in the past 10 years to include not only symmetries acting on higher-dimensional …
expanded in the past 10 years to include not only symmetries acting on higher-dimensional …
Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
DV Else, C Nayak - Physical Review B, 2014 - APS
It is well known that (1+ 1)-dimensional [(1+ 1)-D] bosonic symmetry-protected topological
(SPT) phases with symmetry group G can be identified by the projective representation of …
(SPT) phases with symmetry group G can be identified by the projective representation of …
Symmetry protected topological orders and the group cohomology of their symmetry group
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum
phases with a symmetry G. They can all be smoothly connected to the same trivial product …
phases with a symmetry G. They can all be smoothly connected to the same trivial product …
Introduction to generalized global symmetries in QFT and particle physics
TD Brennan, S Hong - arXiv preprint arXiv:2306.00912, 2023 - arxiv.org
Generalized symmetries (also known as categorical symmetries) is a newly developing
technique for studying quantum field theories. It has given us new insights into the structure …
technique for studying quantum field theories. It has given us new insights into the structure …
Exactly solvable models for symmetry-enriched topological phases
We construct fixed-point wave functions and exactly solvable commuting-projector
Hamiltonians for a large class of bosonic symmetry-enriched topological (SET) phases …
Hamiltonians for a large class of bosonic symmetry-enriched topological (SET) phases …
Topology of nonsymmorphic crystalline insulators and superconductors
Topological classification in our previous paper [K. Shiozaki and M. Sato, Phys. Rev. B 90,
165114 (2014) PRBMDO 1098-0121 10.1103/PhysRevB. 90.165114] is extended to …
165114 (2014) PRBMDO 1098-0121 10.1103/PhysRevB. 90.165114] is extended to …