Majorana zero modes bound to a vortex line in a topological superconductor

We explore Majorana zero modes bound to a vortex line in a three dimensional topological superconductor model, focusing our attention on the validity of the index theorem previously derived. We first solve the Bogoliubov-de Gennes equation at the zero energy to obtain the analytical index. We next calculate the topological index given by the order parameters. It turns out that they indeed coincide and that index theorem, which has been derived on the implicit assumption that a defect is point-like, is also valid for a line defect.Comment: 7 pages, v2: references added, typos corrected, almost final versio

Motivic invariant of real polynomial functions and Newton polyhedron

We propose a computation of real motivic zeta functions for real polynomial functions, using Newton polyhedron. As a consequence we show that the weights are blow-Nash invariants of convenient weighted homogeneous polynomials in three variables.Comment: 22 pages in Math. Proc. Camb. Phil. Soc, 201

SU(\nu) Generalization of Twisted Haldane-Shastry Model

The SU($\nu$) generalized Haldane-Shastry spin chain with $1/r^2$ interaction is studied with twisted boundary conditions. The exact wavefunctions of Jastrow type are obtained for every rational value of the twist angle in unit of $2\pi$. The spectral flow of the ground state is then discussed as a function of the twist angle. By resorting to the motif picture in the Bethe ansatz method, we show that the period of the spectral flow is $\nu$, which is determined by the statistical interaction in exclusion statistics.Comment: 23 pages, revtex, To appear in Nucl. Phys.