Vison States and Confinement Transitions of \(Z_2\) Spin Liquids on the Kagome Lattice

Abstract

We present a projective symmetry group (PSG) analysis of the spinless excitations of \(Z_2\) spin liquids on the kagome lattice. In the simplest case, vortices carrying \(Z_2\) magnetic flux (“visons”) are shown to transform under the 48 element group \(GL(2,Z_3)\). Alternative exchange couplings can also lead to a second case with visons transforming under 288-element group \(GL(2,Z_3)×D_3\). We study the quantum phase transition in which visons condense into confining states with valence bond solid order. The critical field theories and confining states are classified using the vison PSGs.