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

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.