Band gaps in pseudopotential self-consistent GW calculations

For materials which are incorrectly predicted by density functional theory to be metallic, an iterative procedure must be adopted in order to perform GW calculations. In this paper we test two iterative schemes based on the quasi-particle and pseudopotential approximations for a number of inorganic semiconductors whose electronic structures are well known from experiment. Iterating just the quasi-particle energies yields a systematic, but modest overestimate of the band gaps, confirming conclusions drawn earlier for CaB_6 and YH_3. Iterating the quasi-particle wave functions as well gives rise to an imbalance between the Hartree and Fock potentials and results in bandgaps in far poorer agreement with experiment.Comment: 5 pages, 2 figures, 2 table

Semi-regular masas of transfinite length

In 1965 Tauer produced a countably infinite family of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor, no pair of which are conjugate by an automorphism. This was achieved by iterating the process of passing to the algebra generated by the normalisers and, for each $n\in\mathbb N$, finding masas for which this procedure terminates at the $n$-th stage. Such masas are said to have length $n$. In this paper we consider a transfinite version of this idea, giving rise to a notion of ordinal valued length. We show that all countable ordinals arise as lengths of semi-regular masas in the hyperfinite $\mathrm{II}_1$ factor. Furthermore, building on work of Jones and Popa, we obtain all possible combinations of regular inclusions of irreducible subfactors in the normalising tower.Comment: 14 page

A planar calculus for infinite index subfactors

We develop an analog of Jones' planar calculus for II_1-factor bimodules with arbitrary left and right von Neumann dimension. We generalize to bimodules Burns' results on rotations and extremality for infinite index subfactors. These results are obtained without Jones' basic construction and the resulting Jones projections.Comment: 56 pages, many figure