Vestigial anyon condensation in kagome quantum spin liquids

Understand

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 $\mathbb Z_2\boxtimes\mathbb Z_2$ 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.