A bilayer Double Semion Model with Symmetry-Enriched Topological Order

TL;DR

This paper introduces a bilayer Double Semion model that combines topological order with symmetry, leading to fractionalized quasiparticles and novel edge states, advancing the understanding of symmetry-enriched topological phases.

Contribution

It constructs a new bilayer model integrating topological order with flavor symmetry, revealing fractionalization and dual symmetry-protected topological phases.

Findings

Exhibits non-trivial braiding statistics of excitations

Dual model shows symmetry-protected topological order with edge states

Realizes a bilayer non-trivial paramagnet invariant under flavor symmetry

Abstract

We construct a new model of two-dimensional quantum spin systems that combines intrinsic topo- logical orders and a global symmetry called flavour symmetry. It is referred as the bilayer Doubled Semion model (bDS) and is an instance of symmetry-enriched topological order. A honeycomb bi- layer lattice is introduced to combine a Double Semion Topolgical Order with a global spin-flavour symmetry to get the fractionalization of its quasiparticles. The bDS model exhibits non-trival braid- ing self-statistics of excitations and its dual model constitutes a Symmetry-Protected Topological Order with novel edge states. This dual model gives rise to a bilayer Non-Trivial Paramagnet that is invariant under the flavour symmetry and the well-known spin flip symmetry.