Quantum Group Based Theory for Antiferromagnetism and Superconductivity: Proof and Further Evidence

TL;DR

This paper provides a mathematical proof supporting the conjecture that quantum group symmetry unifies antiferromagnetism and high-temperature superconductivity, offering a new perspective beyond classical symmetry models.

Contribution

It offers the first explicit mathematical proof of the quantum group-based model for antiferromagnetism and superconductivity, strengthening the theoretical foundation of this approach.

Findings

Mathematical proof confirms the quantum group conjecture.

Independent calculations support the SO(5) algebra construction.

Quantum group symmetry relates to the d-wave factor and pseudogap behavior.

Abstract

Previously one of us presented a conjecture [APF-4 Proceedings] to model antiferromagnetism and high temperature superconductivity and their 'unification' by quantum group symmetry rather than the corresponding classical symmetry in view of the critique by Baskaran and Anderson of Zhang's classical SO(5) model. This conjecture was further sharpened, experimental evidence and the important role of 1-d systems [stripes] was emphasized and moreover the relationship between quantum groups and strings via WZWN models were given in [Phys. Lett A272, (2000)]. In this brief note we give and discuss mathematical proof of this conjecture, which completes an important part of this idea, since previously an explicit simple mathematical proof was lacking. Moreover an independent calculation [IC/99/2] which constructs the generators forming SO(5) algebra not only supports our previous conjecture but provides a check on our calculations. It is important to note that in terms of physics that the arbitariness [freedom] of the d-wave factor g$^{2}$(k) is tied to quantum group symmetry whereas in order to recover classical SO(5) one must set it to unity in an adhoc manner. We intuitively expect that this freedom may be related to psuedogap behaviour in cuprates.