SU(2) symmetry in a Hubbard model with spin-orbit coupling

TL;DR

This paper investigates the SU(2) symmetry in a spin-orbit coupled Hubbard model, revealing how lattice topology influences whether the symmetry persists or is broken by interactions.

Contribution

It demonstrates that SU(2) symmetry from time-reversal persists in simply-connected lattices with Hubbard interactions but is broken in multi-connected lattices.

Findings

SU(2) symmetry exists without on-site interaction due to time-reversal symmetry

Hubbard interaction preserves symmetry in simply-connected lattices

Hubbard interaction breaks symmetry in multi-connected lattices

Abstract

We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction. It is shown that, in the absence of the on-site interaction, the system possesses the SU(2) symmetry arising from the timereversal symmetry. The influence of the on-site interaction on the symmetry depends on the topology of the networks: The SU(2) symmetry is shown to be the spin rotation symmetry of a simply-connected lattice, so it still holds in the presence of the Hubbard correlation. In contrary, the on-site interaction breaks the SU(2) symmetry of a multi-connected lattice.