Explicit Gauge Fixing for Degenerate Multiplets: A Generic Setup for Topological Orders

TL;DR

This paper develops a general framework for analyzing topological order in multiplets with degeneracies, providing new tools and expressions, including for spin Hall conductance in superconductors, to handle intrinsic degeneracies.

Contribution

It introduces a unified approach for studying topological order in degenerate multiplets, extending standard methods to cases with intrinsic degeneracies and applying it to physical systems.

Findings

New expressions for spin Hall conductance in unitary superconductors

A unified method for topological order with degeneracies

Handling intrinsic degeneracies in topological analysis

Abstract

We supply basic tools for the study of the topological order of a multiplet which is an eigenspace of a finite-dimensional normal operator with continuous parameters. We allow intrinsic degeneracies within the multiplet where a well-known standard procedure does not work. As an important example, we give novel expressions for a spin Hall conductance for unitary superconductors with equal spin pairing. Generic topological orders will be treated in this unified manner particularly with nontrivial topological degeneracies.