time-reversal and cubic symmetries, we show that it is a “parent” state for other exotic states that can be reached by breaking either or both of these: metallic and double-Weyl semi-metallic phases with enormous anomalous Hall effects (AHEs), and topological insulators. We discuss the implications for the iridates at the end of the paper.

The LAB phase itself has striking properties. Its NFL nature is revealed directly by algebraic singularities in the electron spectral function (probed in angle-resolved photoemission) and in optical conductivity, as well as indirectly through many power law thermodynamic and response functions.

![ Phase diagram of the perturbed LAB in the space of renormalized strain to Zeeman field ratio, $\Delta \equiv
  (\delta/H)_R$, versus cubic Zeeman angle, $\theta$. Here“Weyl” denotes the (double) Weyl semimetal, “Ins.” insulator, and “Metal” a metallic phase which has Weyl points shifted from the Fermi energy in the region below the dashed line. For $H=0$, the insulator is a topological insulator. []{data-label="fig1"}](generalPD3.pdf){width="3.3in"}

We now turn to the exposition of these results. We consider the [ *paramagnetic*]{} band structure based on prior work [@ashvin; @ybkim1; @ybkim2], which argued that the states at the zone center ($\Gamma$ point) near the Fermi energy are comprised of the 