SO(5) Symmetry in t-J and Hubbard Models

TL;DR

This paper reviews numerical and analytical evidence supporting SO(5) symmetry as a unifying principle for superconductivity and antiferromagnetism in high-Tc cuprates, linking microscopic models to experimental phenomena.

Contribution

It demonstrates that the low-energy states of the t-J and Hubbard models form SO(5) multiplets, providing a unifying symmetry framework for high-temperature superconductivity.

Findings

SO(5) multiplets are nearly degenerate in the models

D-wave superconducting states derive from SO(5) rotations at half-filling

Experimental signatures include pi-Goldstone modes and spectral relationships

Abstract

Numerical and analytical results are reviewed, which support SO(5) symmetry as a concept unifying superconductivity and antiferromagnetism in the high-temperature superconductors. Exact cluster diagonalizations verify that the low-energy states of the two-dimensional t-J and Hubbard models, widely used microscopic models for the high-Tc cuprates, form SO(5) symmetry multiplets. Apart from a small standard deviation ~J/10, these multiplets become degenerate at a critical chemical potential (transition into doped system). As a consequence, the d-wave superconducting states away from half-filling are obtained from the higher spin states at half-filling through SO(5) rotations. Between one and two dimensions, using weak-coupling renormalization, a rather general ladder Hamiltonian including next-nearest-neighbor hopping can be shown to flow to an SO(5) symmetric point. Experimental tests and consequences such as the existence of a pi-Goldstone mode both in the insulator and superconductor and, in particular, the relationship between the photoemission spectra of the insulator and superconductor, are emphasized.