Non-Abelian Holonomy of BCS and SDW Quasi-particles

TL;DR

This paper explores the non-Abelian SU(2) holonomy of fermionic quasi-particles in high Tc superconductivity within the SO(5) theory, revealing a Yang monopole structure and extending the sigma model to include Dirac fermions coupled to gauge fields.

Contribution

It demonstrates the non-Abelian holonomy of SO(5) spinor states and connects it to the Yang monopole, extending the bosonic sigma model to include fermionic states.

Findings

Identification of non-Abelian SU(2) holonomy in SO(5) fermions

Connection to Yang monopole and second Hopf map

Extension of sigma model with Dirac fermions and gauge fields

Abstract

In this work we investigate properties of fermions in the SO(5) theory of high Tc superconductivity. We show that the adiabatic time evolution of a SO(5) superspin vector leads to a non-Abelian SU(2) holonomy of the SO(5) spinor states. Physically, this non-trivial holonomy arises from the non-zero overlap between the SDW and BCS quasi-particle states. While the usual Berry's phase of a SO(3) spinor is described by a Dirac magnetic monopole at the degeneracy point, the non-Abelian holonomy of a SO(5) spinor is described by a Yang monopole at the degeneracy point, and is deeply related to the existence of the second Hopf map from $S^7$ to $S^4$. We conclude this work by extending the bosonic SO(5) nonlinear sigma model to include the fermionic states around the gap nodes as 4 component Dirac fermions coupled to SU(2) gauge fields in 2+1 dimensions.