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1 results

  • 8 - The Tenfold Way: Gapped Phases in Any Dimensions

  • Christopher Mudry, Paul Scherrer Institute, Villigen, Switzerland, Claudio Chamon, Boston University
  • Book:
    Fractionalization of Particles in Physics
    Published online:
    09 January 2025
    Print publication:
    23 January 2025, pp 745-856

  • Summary

    Chapter 8 extends the 10-fold way of gapped phases from one to any dimension of space. This is done by presenting the homotopy groups of the classifying spaces of normalized Dirac masses. There follows two applications. First, there is the interplay between Anderson localization and the topology of classifying spaces for disordered quantum wires. Second, it is possible to derive the breakdown of the 10-fold way due to short-range interactions in any dimension. The chapter closes with the relationship between invertible topological phases and invertible topological field theories.