A Microscopic Derivation of the SO(5)-Symmetric Landau-Ginzburg Potential

TL;DR

This paper derives a microscopic model that explains the coexistence and competition of superconductivity and antiferromagnetism with an approximate SO(5) symmetry, reproducing phase diagrams similar to cuprates.

Contribution

It provides a microscopic derivation of the SO(5)-symmetric Landau-Ginzburg potential from electron interactions, linking microscopic physics to macroscopic phase behavior.

Findings

Phase diagram resembles that of cuprates.

Antiferromagnetism can be incommensurate with doping.

Explicit integration of fermions yields the Landau-Ginzburg free energy.

Abstract

We construct a microscopic model of electron interactions which gives rise to both superconductivity and antiferromagnetism, and which admits an approximate SO(5) symmetry that relates these two phases. The symmetry can be exact, or it may exist only in the long-wavelength limit, depending on the detailed form of the interactions. We compute the macroscopic Landau-Ginzburg free energy for this model as a function of temperature and doping, by explicitly integrating out the fermions. We find that the resulting phase diagram can resemble that observed for the cuprates, with the antiferromagnetism realized as a spin density wave, whose wavelength might be incommensurate with the lattice spacing away from half filling.