On the Classification of Topological Orders
Sign Up to like & getrecommendations! Published in 2022 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-022-04380-3
Abstract: We axiomatize the extended operators in topological orders (possibly gravitationally anomalous, possibly with degenerate ground states) in terms of monoidal Karoubi-complete $n$-categories which are mildly dualizable and have trivial centre. Dualizability encodes the word "topological,"… read more here.
Keywords: topological orders; classification topological;
On the classification of topological quandles
Sign Up to like & getrecommendations! Published in 2018 at "Topology and its Applications"
DOI: 10.1016/j.topol.2018.08.011
Abstract: We investigate the classification of topological quandles on some simple manifolds. Precisely we classify all Alexander quandle structures, up to isomorphism, on the real line and the unit circle. For the closed unit interval $[0,… read more here.
Keywords: topology; classification topological; topological quandles;
Classification of topological insulators and superconductors out of equilibrium
Sign Up to like & getrecommendations! Published in 2019 at "Physical Review B"
DOI: 10.1103/physrevb.99.075148
Abstract: We establish the existence of a topological classification of many-particle quantum systems undergoing unitary time evolution. The classification naturally inherits phenomenology familiar from equilibrium -- it is robust against disorder and interactions, and exhibits a… read more here.
Keywords: topological insulators; classification topological; insulators superconductors; equilibrium classification ... See more keywords