Phase diagrams for θ=π and θ=2π/3

1. eiθ Condensations of particles with mutual statisticsOlexei Motrunich, California Institute of Technology, DMR 0907145 One of the crucial properties of topological quantum phases is that they have excitations with unusual statistics. By studying possible condensation patterns of such excitations, we can understand possible proximate phases and phase transitions. Carrying out such a program is challenging since the unusual statistics implies quantum interferences that confound our intuition. With student Scott Geraedts, we explored a particular example in 2+1 space-time dimensions with two species of particles that are bosons by themselves but have mutual statistics characterized by a statistical angle θ. We examined in detail two representative cases of θ=π and θ=2π/3 and provided complete understanding of the rich phase diagrams by a combination of numerical Monte Carlo and analytical duality methods. Cross-linking of loops like in the chain-mail image on the left is crucial in our model, which is defined so that there is a phase eiθfor each cross-linking of the world-lines of the two species of particles. θ=π θ=2π/3 Phase diagrams for θ=π and θ=2π/3

2. Condensations of particles with mutual statisticsOlexei Motrunich, California Institute of Technology, DMR 0907145 * During the 2011-2012 academic year, this award supported research of two graduate students at Caltech, Hsin-Hua Lai and Scott Geraedts. Both students presented their work at the APS March meeting in Boston. Hsin-Hual Lai defended his PhD thesis in May 2012 and is starting a postdoctoral position at the National High Magnetic Field Laboratory in Tallahassee. The award also supported PI's collaborations with researchers including postdocs and students at University of California-Santa Barbara and California State University-Northridge. The PI participated and presented results of the research at international workshops in Dresden and Stockholm.