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

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.Comment: 10 pages, no figure

Flow Equations and Normal Ordering

In this paper we consider flow-equations where we allow a normal ordering which is adjusted to the one-particle energy of the Hamiltonian. We show that this flow converges nearly always to the stable phase. Starting out from the symmetric Hamiltonian and symmetry-broken normal ordering nearly always yields symmetry breaking below the critical temperature.Comment: 7 page

Inhomogeneous Fixed Point Ensembles Revisited

The density of states of disordered systems in the Wigner-Dyson classes approaches some finite non-zero value at the mobility edge, whereas the density of states in systems of the chiral and Bogolubov-de Gennes classes shows a divergent or vanishing behavior in the band centre. Such types of behavior were classified as homogeneous and inhomogeneous fixed point ensembles within a real-space renormalization group approach. For the latter ensembles the scaling law $\mu=d\nu-1$ was derived for the power laws of the density of states $\rho\propto|E|^\mu$ and of the localization length $\xi\propto|E|^{-\nu}$. This prediction from 1976 is checked against explicit results obtained meanwhile.Comment: Submitted to 'World Scientific' for the volume 'Fifty Years of Anderson Localization'. 12 page