Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons

Bachmann, Sven (2017): Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons. In: Reviews in Mathematical Physics, Vol. 29, No. 6, 1750018

Abstract

In this comprehensive study of Kitaev's abelian models defined on a graph embedded on a closed orientable surface, we provide complete proofs of the topological ground state degeneracy, the absence of local order parameters, compute the entanglement entropy exactly and characterize the elementary anyonic excitations. The homology and cohomology groups of the cell complex play a central role and allow for a rigorous understanding of the relations between the above characterizations of topological order.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0129-055X
• Language: English