Fractional Abelian topological phases of matter for fermions in two-dimensional space

TL;DR

This paper reviews topological phases of matter for fermions in two dimensions, focusing on the tenfold way classification, chiral Abelian bosonization, and the construction of 2D topological phases from coupled wires.

Contribution

It introduces a comprehensive review of the tenfold way, bosonization techniques, and methods to build 2D topological phases from wire models, advancing understanding of topological matter.

Findings

Analysis of edge stability in symmetry class AII

Construction methods for 2D topological phases from coupled wires

Application of chiral Abelian bosonization to topological phases

Abstract

These notes constitute chapter 7 from "l'Ecole de Physique des Houches" Session CIII, August 2014 dedicated to Topological Aspects of Condensed matter physics. The tenfold way in quasi-one-dimensional space is presented. The method of chiral Abelian bosonization is reviewed. It is then applied to the stability analysis for the edge theory in symmetry class AII, and for the construction of two-dimensional topological phases from coupled wires.