Asymmetry protected emergent E8 symmetry



Playing this video requires the latest flash player from Adobe.

Download link (right click and 'save-as') for playing in VLC or other f4v compatible player.


Recording Details

Speaker(s): 
Scientific Areas: 
PIRSA Number: 
13050027

Abstract

The E8 state of bosons is a 2+1d gapped phase of matter which has no topological entanglement entropy but has protected chiral edge states in the absence of any symmetry.  This peculiar state is interesting in part because it sits at the boundary between short- and long-range entangled phases of matter.  When the system is translation invariant and for special choices of parameters, the edge states form the chiral half of a 1+1d conformal field theory - an E8 level 1 Wess-Zumino-Witten model.  However, in general the velocities of different edge channels are different and the system does not have conformal symmetry.  We show that by considering the most general microscopic Hamiltonian, in particular by relaxing the constraint of translation invariance and adding disorder, conformal symmetry remerges in the low energy limit.  The disordered fixed point has all velocities equal and is the E8 level 1 WZW model.  Hence a highly entangled and highly symmetric system emerges, but only when the microscopic Hamiltonian is completely asymmetric.