Renormalization - group properties of some vertex models

Yasushi Honda, Tsuyoshi Horiguchi

Bruce W. Westbury

Mitra, Saibal

In this thesis we use renormalization group methods to study the critical behaviour of the staggered F-model. This model is a six vertex model that can be used to calculate the thermodynamic properties of a facet of a BCC crystal in the (100) direction.

H. J. F. Knops

Hiroshi Takasaki, Tomotoshi Nishino, Yasuhiro Hieida

Phase diagram of a symmetric vertex model which allows 7 vertex configurations is obtained by use of the corner transfer matrix renormalization group (CTMRG), which is a variant of the density matrix renormalization group (DMRG). The critical indices of this model are identified as $β= 1/8$ and $α= 0$.

Stefan Maier, Carsten Honerkamp A, Qiang-Hua Wang

We analyze the point-group symmetries of generic multiband tight-binding models with respect to the transformation properties of the effective interactions. While the vertex functions in the orbital language may transform non-trivially under point-group operations, their point-group behavior in the band language can be simplified by choosing a suitable Bloch basis. We first give two analytically accessible examples. Then, we show that, for a large class of models, a natural Bloch basis exists, in which the vertex functions in the band language transform trivially under all point-group operations. As a consequence, the point-group symmetries can be used to reduce the computational effort in perturbative many-particle approaches, such as the functional renormalization group.