Vestigial anyon condensation in kagome quantum spin liquids

TL;DR

This paper models kagome quantum spin liquids and uncovers a three-stage anyon condensation process through quantum Monte Carlo simulations, illustrating phase transitions between different topological orders in quantum magnets.

Contribution

It introduces a lattice model of topological order and demonstrates vestigial anyon condensation with unbiased numerical solutions, providing a new platform for studying topological phase transitions.

Findings

Identified a three-stage anyon condensation process.

Observed transitions from $ ext{Z}_2 imes ext{Z}_2$ to $ ext{Z}_2$ topological order.

Revealed a transition to a trivial symmetric phase.

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 $\mathbb Z_2\boxtimes\mathbb Z_2$ 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.