Symposium on Topological Quantum Computation 4-5 June 2011 Nordita
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Kaleidoscope of topological phases with multiple Majorana species (Janik Kailasvuori, MPI Dresden)

 Exactly solvable lattice models for spins or hopping fermions provide fascinating examples of topological phases. Some of them support localized Majorana fermions, which feature in topologically protected quantum computing. The Chern invariant $\nu$ is one important characterization of such phases. Systems with arbitrarily large Chern numbers are known, but systems supporting Majorana fermions have mainly provided ground states with $\nu=0,\pm1$ although symmetry arguments in some cases allow for any integer $\nu$. With the rich variety of phases exhibited by spin-triplet p-wave fermions in mind, we look at the square-octagon variant of Kitaev's honeycomb model. It maps to spinful paired fermions and indeed 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. We show that transitions between topological phases are accompanied by stepwise transfer of Chern number between the four bands and then finally describe the edge spectra at topological domain walls, highlighting the one between distinct $\nu=0$ phases.

Id: 254
Place: Nordita
Roslagstullsbacken 23
106 91 Stockholm
Sweden

Room: 132:028
Starting date:
 04-Jun-2011 15:00
Duration: 45'

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