Non-Abelian vortices in the emergent U(2) gauge theory of the Hubbard model

TL;DR

This paper constructs non-Abelian vortex solutions within a U(2) gauge theory derived from the Hubbard model on a honeycomb lattice, revealing novel flux quantization and zero mode properties relevant to condensed matter phases.

Contribution

It introduces the first explicit construction of non-Abelian vortices in the emergent U(2) gauge theory of the Hubbard model, linking vortex solutions to different quantum phases.

Findings

Magnetic flux quanta are half-integer.

Each vortex hosts two bosonic zero modes.

Single vortex has two fermionic zero energy states.

Abstract

By the spin-fermion formula, the Hubbard model on the honeycomb lattice is represented by a U(2) gauge theory in the mean field method, non-Abelian vortex solutions are constructed based on this theory. The quantization condition shows that the magnetic flux quanta are half-integer. There are $2k$ bosonic zero modes for $k$ winding vortices. For the fermions, there are 2 zero energy states (ZESs) corresponding to the single elementary vortex. In the vortex core and on the edge, the system are in the semi-metal phase with a spin gap and in the insulator phase with N\'eel order phase, and can be mapped to the superconductor in class A and CI, respectively.