algebras in quantum theory bk chapter

Doron Gepner

We construct new solvable vertex models based on the spin representation of the Lie algebra Bk. We use these models to study the algebraic structure underlying such vertex theories. We show that all the Bk spin vertex models obey a version of the BMW algebra along with extra relations that are called n–CB (conformal braiding) algebras. These algebras were discussed before for various IRF (interaction round the face) models. Here we establish that the same algebras hold for vertex models.

Vasily Evgenevich Tarasov

Alexander A. Belavin, Doron Gepner, Hans Wenzl

We describe the Boltzmann weights of the Dk algebra spin vertex models. Thus, we find the SO(N) spin vertex models, for any N, completing the Bk case found earlier. We further check that the real (self–dual) SO(N) models obey quantum algebras, which are the Birman–Murakami–Wenzl (BMW) algebra for three blocks, and certain generalizations, which include the BMW algebra as a sub–algebra, for four and five blocks. In the case of five blocks, the B4 model is shown to satisfy additional twenty new relations, which are given. The D6 model is shown to obey two additional relations.

雄一郎 北島

Valter Moretti

George Kastrinakis

"This thesis consists of three Chapters. In the first Chapter, based on a planar unconventional Fermi liquid model, we present several results on the optimally doped and overdoped cuprate superconductors. For the normal state, we have analytically derived a linear in temperature and energy scattering rate for the carriers. This scattering rate yields necessarily a linear in temperature resistivity and a linear in 1/energy optical conductivity. The linearity of the scattering rate requires that the interacting Fermi liquid has strong peaks in its density of states (van-Hove singularities in 2 dimensions) near the chemical potential fl· Our results are backed by self-consistent Baym-Kadanoff (BK) numerical calculations, which also show that the interactions tend to pin the van- Hove singularities close to fl· We show that the low energy dependence of the Millis-Monien- Pines susceptibility XMMP can have a fermionic origin. We obtain particularly high transition temperatures Tc from our BK-Eliashberg scheme by introducing an ansatz for the susceptibility of the carriers. We postulate that the latter is enhanced in an additive manner due to the weak antiferromagnetic order of the Cu02 planes. Thus we have obtained a dx2_y2 gap with Tc > 120°K for nearest neighbor hopping t = 250me V. In the second Chapter we propose a novel mechanism for giant corrections to the transport quantities, including positive giant magnetoresistance, due to the presence of paramagnons in a weakly disordered metal. At low temperature and for finite impurity spin scattering, for a certain value, predicted from our theory, of the material-dependent paramagnon interaction, the total conductivity becomes highly sensitive to the orbital effects of a finite magnetic field. This is attributed to certain microscopic processes, otherwise negligibly small, which can be enhanced by a resonance factor, emanating from· the spin-density channel. We obtain very good agreement between this theory and four (4) different positive giant magnetoresistance experiments, including very recent ones, while making specific material-dependent predictions. We emphasize that our theory broadens the 'conventional wisdom' viewpoint that weak disorder would only generate small corrections to transport quantities. In the third Chapter we examine the effects of interface roughness and/or planar impurity doping in a superlattice, under the assumption that a weak disorder description is adequate. We find that these two types of disorder are equivalent, and that they can be viewed as effective ""bulk"" disorder, with anisotropic diffusion coefficients. This study can offer quantitative insight to transport properties of multilayers and devices, which contain inadvertently structural disorder at the interfaces."