Vestigial anyon condensation in kagome quantum spin liquids

Abstract

We construct a lattice model of topological order (kagome quantum spin liquids) and solve it with unbiased quantum Monte Carlo simulations. A three-stage anyon condensation with two transitions from a ${\mathbb{Z}}_2⊠{\mathbb{Z}}_2$ topological order to a ${\mathbb{Z}}_2$ topological order and eventually to a trivial symmetric phase is revealed. These results provide concrete examples of phase transitions between topological orders in quantum magnets. The designed quantum spin liquid model and its numerical solution offer a playground for further investigations on vestigial anyon condensation.

7 pages, 9 figures