Finite-Size Studies on the SO(5) Symmetry of the Hubbard Model

TL;DR

This paper provides numerical evidence supporting the approximate SO(5) symmetry in the Hubbard model on a small cluster, linking it to experimental neutron scattering observations in YBCO superconductors.

Contribution

It demonstrates the presence of SO(5) symmetry in a finite-size Hubbard model and connects theoretical findings to experimental data.

Findings

Sharp collective peaks in dynamic correlation functions involving $\pi$ operators.

Support for interpreting neutron scattering peaks as Goldstone modes of SO(5) symmetry.

Numerical evidence of approximate SO(5) symmetry in a 10-site Hubbard cluster.

Abstract

We present numerical evidence for the approximate SO(5) symmetry of the Hubbard model on a 10 site cluster. Various dynamic correlation functions involving the $\pi$ operators, the generators of the SO(5) algebra, are studied using exact diagonalisation, and are found to possess sharp collective peaks. Our numerical results also lend support on the interpretation of the recent resonant neutron scattering peaks in the YBCO superconductors in terms of the Goldstone modes of the spontaneously broken SO(5) symmetry.