Topological Defects

Cambridge University Press eBooks, pp. 113–132

Abstract

In this chapter, we introduce topological defects as excitations complementary to the elementary Nambu–Goldstone modes and relate their classification to the presence of broken symmetries. We show that the proliferation of topological defects can lead to the suppression of long-range correlations and the emergence of algebraic long-range order. The Berezinskii–Kosterlitz–Thouless phase transition is discussed both generally and in the specific example of the one-dimensional Ising model. In the same context, the Kramers–Wannier duality between topological defects and elementary modes is introduced.

Authors 3

1. Aron J. Beekman
   Affiliation as printed

   Sioux Technologies

2. Louk Rademaker Aachen

   Leiden University · University of Geneva

   Affiliation as printed

   University of Geneva and Leiden University

3. Jasper van Wezel

   University of Amsterdam

   Affiliation as printed

   University of Amsterdam