Diabolical textures from spatially embedded Thouless pumps yield distinct gapped states separated by trap-scaling critical points that terminate into unnecessary critical surfaces when the texture varies rapidly, with a classification framework based on Kitaev's Ω spectrum conjecture.
On the classification of topological defects and textures
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
Ordered phases resulting from spontaneously broken continuous symmetries are effectively described by sigma models of maps to the coset space of Goldstone modes. A classic problem is to classify the topological sectors of the sigma model. In simple cases, this can be expressed in terms of homotopy groups of the target space; but in general, it is a complicated affair -- even in two dimensions -- and a general method is lacking. In this letter, we introduce a technique to systematically classify topological sectors of sigma models in various dimensions using a framework based on higher categorical generalizations of the fundamental group. As a demonstration, we recover some known results and obtain new ones. The technique and relevant mathematical structures are described only qualitatively in this letter; details can be found in our companion paper.
fields
cond-mat.str-el 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Topological Phenomena Protected by Diabolical Textures
Diabolical textures from spatially embedded Thouless pumps yield distinct gapped states separated by trap-scaling critical points that terminate into unnecessary critical surfaces when the texture varies rapidly, with a classification framework based on Kitaev's Ω spectrum conjecture.