We show that generic SU(2)-invariant random spin-1 chains have phases with an emergent SU(3) symmetry. We map out the full zero-temperature phase diagram and identify two different phases: (i) a conventional random singlet phase (RSP) of strongly bound spin pairs (SU(3) "mesons") and (ii) an unconventional RSP of bound SU(3) "baryons", which are formed, in the great majority, by spin trios located at random positions. The emergent SU(3) symmetry dictates that susceptibilities and correlation functions of both dipolar and quadrupolar spin operators have the same asymptotic behavior.

Recently, a new group of layered transition-metal tetra-chalcogenides was proposed via first principles calculations to correspond to a new family of Weyl type-II semimetals with promising topological properties in the bulk as well as in the monolayer limit. In this article, we present measurements of the Shubnikov-de Haas (SdH) and de Haas-van Alphen effects under high magnetic fields for the type-II Weyl semimetallic candidate NbIrTe4. We find that the angular dependence of the observed Fermi surface extremal cross-sectional areas agree well with our DFT calculations supporting the existence of Weyl type-II points in this material. Although we observe a large and non-saturating magnetoresistivity in NbIrTe4 under fields all the way up to 35 T, Hall-effect measurements indicate that NbIrTe4 is not a compensated semimetal. The transverse magnetoresistivity displays a fourfold angular dependence akin to the so-called butterfly magnetoresistivity observed in nodal line semimetals. We conclude that the field and this unconventional angular-dependence are governed by the topography of the Fermi-surface and the resulting anisotropy in effective masses and in carrier mobilities.

The Flow Equation Method was proposed by Wegner as a technique for studying interacting systems in one dimension. Here, we apply this method to a disordered one dimensional model with power-law decaying hoppings. This model presents a transition as function of the decaying exponent α. We derive the flow equations, and the evolution of single-particle operators. The flow equation reveals the delocalized nature of the states for α < 1/2. Additionally, in the regime, α > 1/2, we present a strong-bond renormalization group structure based on iterating the three-site clusters, where we solve the flow equations perturbatively. This renormalization group approach allows us to probe the critical point (α = 1). This method correctly reproduces the critical level-spacing statistics, and the fractal dimensionality of the eigenfunctions.