We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically doped 3D topological insulator, separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite ch...

A discrete version of the Zak transform is defined and used to analyze discrete Weyl–Heisenberg frames, which are nonorthogonal systems in the space of square-summable sequences that, although not necessarily bases, provide representations of square-summable sequences as sums of the frame elements. While the general theory is essentially similar to the continuous case, major differences occur w...

Weyl semimetals (WSMs) constitute a 3D phase with linearly dispersing Weyl excitations at low energy, which lead to unusual electrodynamic responses and open Fermi arcs on boundaries. We derive a simple criterion to identify and characterize WSMs in an interacting setting using the exact electronic Green's function at zero frequency, which defines a topological Bloch Hamiltonian. We apply this ...

Given a root system Φ of rank r and a global field F containing the n-th roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose coefficients are n-th order Gauss sums. It is a function of r complex variables, and it has meromorphic continuation to all of C, with functional equations forming a group isomorphic to the Weyl group of Φ. Weyl group multiple Dirichlet s...

We review firstly whyWeyl’s Geometry, within the context of FriedmanLemaitre-Robertson-Walker cosmological models, can account for both the origins and the value of the observed vacuum energy density (dark energy). The source of dark energy is just the dilaton-like Jordan-BransDicke scalar field that is required to implement Weyl invariance of the most simple of all possible actions. A nonvanis...

This paper considers Weyl modules for a simple, simply connected algebraic group over an algebraically closed field k of positive characteristic p 6= 2. The main result proves, if p ≥ 2h− 2 (where h is the Coxeter number) and if the Lusztig character formula holds for all (irreducible modules with) regular restricted highest weights, then any Weyl module ∆(λ) has a ∆-filtration, namely, a filtr...

We study a second example of the phenomenon studied in the article “The complex Lorentzian Leech lattice and the bimonster”. We find 14 roots in the automorphism group of the the quaternionic Lorentzian Leech lattice L that form the Coxeter diagram given by the incidence graph of projective plane over F2. We prove that the reflections in these 14 roots generate the automorphism group of L. The ...