Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice

We theoretically study an exactly solvable Gamma matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with "expanded" vertices and links. We find this model displays an exceptionally rich phase diagram that includes: (i) gapless phases with stable spin fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points, and (iii) gapped phases with finite Chern numbers possessing the values {\pm}4,{\pm}3,{\pm}2 and {\pm}1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit when these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results highlight the richness of possible ground states in closely related magnetic systems.Comment: 9 pages, 9 figure

Kaleidoscope of topological phases with multiple Majorana species

Exactly solvable lattice models for spins and non-interacting fermions provide fascinating examples of topological phases, some of them exhibiting the localized Majorana fermions that feature in proposals for topological quantum computing. The Chern invariant $\nu$ is one important characterization of such phases. Here we look at the square-octagon variant of Kitaev's honeycomb model. It maps to spinful paired fermions and enjoys a rich phase diagram featuring distinct abelian and nonabelian phases with $\nu= 0,\pm1,\pm2,\pm3$ and $\pm4$. The $\nu=\pm1$ and $\nu=\pm3$ phases all support localized Majorana modes and are examples of Ising and $SU(2)_2$ anyon theories respectively.Comment: 6 pages, 5 figures. The second version has a new title, reflecting a change of focus of the presentation in this version. The third version contains minor changes and is essentially the one published in New Journal of Physic

The theoretical prediction of the boundary-layer-blockage and external flow choking at moving aircraft in ground effects

The theoretical discoveries of the Sanal flow choking [V. R. Sanal Kumar et al., "Sanal flow choking: A paradigm shift in computational fluid dynamics code verification and diagnosing detonation and hemorrhage in real-world fluid-flow systems,"Global Challenges 4, 2000012 (2020)] and streamtube flow choking [V. R. Sanal Kumar et al., "Deflagration to detonation transition in chemical rockets with sudden expansion/divergence regions,"AIAA Paper No. 2020-3520, 2020] achieved significant contemplation in all branches of science and engineering for resolving various unanswered scientific questions brought onward from the beginning of this era [V. R. Sanal Kumar et al., "A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers,"AIP Adv. 8, 025315 (2018)]. The applications of these flow choking phenomena are more significant in aerospace industries [V. R. Sanal Kumar et al., "Nanoscale flow choking and spaceflight effects on cardiovascular risk of astronauts - A new perspective,"AIAA Paper No. 2021-0357, 2021] and medical sciences [V. R. Sanal Kumar et al., "Lopsided blood-thinning drug increases the risk of internal flow choking leading to shock wave generation causing asymptomatic cardiovascular disease,"Global Challenges 2021, 2000076]. Herein, as an offshoot of the Sanal flow choking phenomena, the proof of the concept of boundary-layer-blockage (BLB) persuaded external-flow-choking (EFC) at aircraft-in-ground (AIG)-effect is presented. When the aircraft's ground clearance is relatively low, the evolving BLB factor from both planes (the bottom surface of the aircraft and the ground) creates a transient fluid-throat, leading to the Sanal flow choking and supersonic flow development in the duct flow region. In this physical situation, the pressure ratio (Ptotal/Pstatic) at the external flow choking region is exclusively a function of the specific heat ratio of the fluid. The EFC is more prone for the low wing aircraft flying in the near vicinity to the ground and/or sea with relatively high subsonic Mach number and low angle of attack. At this flying condition, the underside of the aircraft (fuselage and/or wing) and the ground creates the convergent-divergent duct flow effect leading to the EFC at the critical total-to-static pressure ratio. The accurate estimation of the BLB factor at the location of the EFC at AIG effect is presented in this manuscript as a universal yardstick for two-dimensional (2D) in silico simulation. For establishing the proof of the concept of external flow choking and supersonic flow development and shock wave generation, the 2D in silico results are presented for both stationary and moving airfoils in ground effect. In silico results show that the airfoil at stationary position exhibits relatively higher BLB factor and an immediate occurrence of the EFC than the same airfoil moving with the identical inflow Mach number and Reynolds number. We could establish herein that the moving vehicle simulation is inevitable for capturing actual flow physics and further precise examination of the BLB factor and the possibilities of the occurrence of the EFC for credible trajectory optimization of high-speed ground-effect vehicles. © 2021 Author(s).12 month embargo; published online: 11 March 2021This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]