Kaleidoscope of topological phases in an exactly solvable spin model

Date

Feb 10, 2011

Time

2:00 PM - 3:00 PM

Speaker

Graham Kells

Affiliation

Berlin

Language

en

Main Topic

Physik

Other Topics

Physik

Description

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 phase space of 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 non-abelian 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.

Last modified: Feb 9, 2011, 10:29:10 AM