From Antiferromagnetism to Superconductivity: Numerical Evidence for SO(5) Symmetry

TL;DR

This paper provides numerical evidence supporting the SO(5) symmetry as a unifying framework for superconductivity and antiferromagnetism in high-temperature superconductors, using exact diagonalization of the t-J model.

Contribution

It verifies the SO(5) multiplet structure in the t-J model and demonstrates the robustness of SO(5) symmetry against various perturbations.

Findings

d-wave superconducting states relate to half-filling states via SO(5) rotations

the pi-resonance is the dominant low-energy feature across doping levels

SO(5) symmetry remains stable with Coulomb and next-nearest neighbor interactions

Abstract

In this work, we present numerical results which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Using exact cluster diagonalization, we verify the recently proposed SO(5) multiplet structures for a widely used microscopic model, the t-J model. Our results show that the d-wave superconducting ground states away from half-filling are obtained from the higher spin states at half-filling through SO(5) rotations, that the dominant low energy resonance in the dynamical spin correlation function corresponds to a `pi-resonance' in the entire low doping region, and that the SO(5) symmetry is robust against inclusion of longer ranged Coulomb repulsion and next-nearest neighbor hopping.