# Dresden 2014 – wissenschaftliches Programm

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# HL: Fachverband Halbleiterphysik

## HL 90: Low-dimensional systems: Topological order (organized by TT)

### HL 90.10: Vortrag

### Donnerstag, 3. April 2014, 12:15–12:30, HSZ 204

**Detection of symmetry enriched topological phases** — •Ching-Yu Huang^{1}, Xie Chen^{2}, and Frank Pollmann^{1} — ^{1}Max Planck Institute for the Physics of Complex Systems, Dresden, Germany — ^{2}Department of Physics, University of California, Berkeley, California, USA

Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry enriched topological (SET) phases. We introduce simple methods to detect the SET order directly from a complete set of topologically degenerate ground state wave functions. In particular, we first show how to directly determine the characteristic symmetry fractionalization of the quasiparticles from the reduced density matrix of the minimally entangled states. Second, we show how a simple generalization of a string order parameter can be measured to detect SET. The selection rules will get a characterization of SET. This way is more physical, and can be used by other methods, e.g., quantum Monte Carlo methods or potentially measured experimentally. We demonstrated the usefulness of this approach by considering first a spin-1 model on the honeycomb lattice and the resonating valence bond state on a kagome lattice.