Orthogonality constraints and entropy in the SO(5)-Theory of HighT_c-Superconductivity

TL;DR

This paper critiques Zhang's SO(5) theory of high-temperature superconductivity, showing that orthogonality constraints, which maximize entropy at finite temperature, are key to understanding the effective interactions and phase competition.

Contribution

It clarifies the role of orthogonality constraints in the SO(5) theory and challenges Zhang's derivation of the effective interaction, offering a new perspective on the theory's foundations.

Findings

Orthogonality constraints maximize entropy at finite temperature.

Ground states obey orthogonality constraints when driven by interactions.

Effective interaction similar to Zhang's is obtained via orthogonality constraints.

Abstract

S.C. Zhang has put forward the idea that high-temperature-superconductors can be described in the framework of an SO(5)-symmetric theory in which the three components of the antiferromagnetic order-parameter and the two components of the two-particle condensate form a five-component order-parameter with SO(5) symmetry. Interactions small in comparison to this strong interaction introduce anisotropies into the SO(5)-space and determine whether it is favorable for the system to be superconducting or antiferromagnetic. Here the view is expressed that Zhang's derivation of the effective interaction V_{eff} based on his Hamiltonian H_a is not correct. However, the orthogonality constraints introduced several pages after this 'derivation' give the key to an effective interaction very similar to that given by Zhang. It is shown that the orthogonality constraints are not rigorous constraints, but they maximize the entropy at finite temperature. If the interaction drives the ground-state to the largest possible eigenvalues of the operators under consideration (antiferromagnetic ordering, superconducting condensate, etc.), then the orthogonality constraints are obeyed by the ground-state, too.