The Spectrum-Generating Algebra of the Van Hove Scenario is SO(8)

TL;DR

This paper demonstrates that the complex instabilities in the Van Hove scenario can be unified under an SO(8) algebra, revealing a comprehensive symmetry framework for various phases including superconductivity and striped phases.

Contribution

It introduces an SO(8) spectrum-generating algebra that classifies all nesting and pairing instabilities in the Van Hove scenario, extending previous symmetry groups.

Findings

SO(6) subgroup acts as an approximate symmetry group

Contains SO(5) and SO(4) as subgroups, linking to previous models

Describes both striped phases and superconductivity within a unified framework

Abstract

The various nesting and pairing instabilities of the generalized Van Hove scenario can be classified via an SO(8) spectrum-generating algebra. An SO(6) subgroup is an approximate symmetry group of the model, having two 6-dimensional representations (`superspins'). This group contains as subgroups both the SO(5) and SO(4) groups found by Zhang, while one superspin is a combination of Zhang's 5-component superspin with a flux phase instability; the other includes a charge density wave instability plus s-wave superconductivity. This is the smallest group which can describe both striped phases and superconductivity.