The choice of the symmetry group for the cuprates

TL;DR

This paper proposes using the classical symmetry group SO(7) to model the complex phenomena in cuprates, including antiferromagnetism, superconductivity, and various competing phases, within a quantum symmetry framework.

Contribution

It introduces a specific classical symmetry group choice, SO(7), to underpin a quantum symmetry model for cuprates, encompassing multiple phases and phenomena.

Findings

SO(7) accommodates multiple competing phases in cuprates

The model links pseudo-gap phenomena with lattice distortions

Symmetry choice influences understanding of cuprate phase behavior

Abstract

Following our recent conjecture to model the phenomenona of antiferromagnetism and superconductivity by quantum symmetry groups, we discuss in the present note the choice of the classical symmetry group underlying the quantum group. Keeping in mind the degrees of freedom arising from spin, charge, and lattice we choose the classical group as SO(7). This choice is also motivated to accomodate the several competing phases which are or may be present in these and related materials, such as stripe phase [mesoscopically ordered phase], Luttinger liquids, nearly antiferromagnetic Fermi liquids, charge-ordered Fermi liquids, glassy phase, stringy phase and perhaps more. The existence and the behavior of pseudo-gap and lattice distortion are also an important consideration. We have lumped the charge, spin and lattice-distortion ordering and other orderings into the psuedogap.