#### Special Seminar - Matthias Troyer, ETH, Zurich: "Interacting Anyons in Topological Quantum Liquids: Variations on the 'golden chain' "

We discuss generalizations of fermionic quantum lattice models using anyonic degrees of freedom. The simplest model for interacting anyons, the golden chain energetically favors neighboring localized anyons to fuse into the trivial channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of the anyonic generalization of spin-1/2 chains show that these models are critical and described by two-dimensional (2D) conformal field theories and are direct realizations of the unitary minimal models of conformal field theory.

I will then discuss generalizations of this simplest model: with longer range interactions and spin-1 chains we obtain anyonic generalizations of the corresponding quantum spin models. Going to two dimensions we find that instead of SU(2)-symmetry breaking ordered phases in case of spins the ground states of the anyonic models are gapped quantum Hall states with gapless edge modes corresponding to the edge states between two different quantum Hall liquids. Making the anyons mobile in a generalization of a t-J model we find the equivalent of spin-charge separation in Luttinger liquids.

Host: Shivaji Sondhi

**Location:**
Jadwin 303

**Date/Time: **03/28/14
at
1:30 pm
- 03/28/14
at
2:30 pm

**Category: **Special Seminar

**Department: **Physics