Topological Quantum Dimers Emerging from Kitaev Spin Liquid Bilayer: Anyon Condensation Transition*

Quantum Spin Liquids (QSLs) are many-body quantum entangled states supporting anyon quasiparticles, proposed as one of the best platforms for quantum science and technology. In particular, Kitaev Spin Liquid (KSL) and Resonating Valence Bond (RVB) states are active subjects of research, stimulated by recent advances in experimental platforms including the quantum magnet RuCl3, quantum processors, and Rydberg atom arrays.

Transition mechanism between distinct QSLs is one of the outstanding problems in the field of topological quantum matter. Anyon condensation was theoretically proposed as a mechanism for such transitions, providing global insights on how a variety of topological phases can be connected via anyon condensation transitions. However, it has been elusive to confirm the mechanism in quantum spin systems because of the scarcity of appropriate microscopic models and the difficulty with defining an order parameter for anyon condensation in terms of local spin operators.

In this work, I introduce a bilayer spin model that illuminates the mechanism of anyon condensation transition. KSL bilayer state and RVB state are stabilized in different limits of the model, connected by an anyon condensation transition. By performing explicit calculations of the order parameter, this work provides numerical evidence for the anyon condensation and uncovers an intimate connection between the KSL bilayer and RVB states.