  Transitions between quantum spin liquids (QSLs) are fundamental problems
lying beyond the Landau paradigm and requiring a deep understanding of the
entanglement structures of QSLs called topological orders. The novel concept of
anyon condensation has been proposed as a theoretical mechanism, predicting
various possible transitions between topological orders, but it has long been
elusive to confirm the mechanism in quantum spin systems. Here, we introduce a
concrete spin model that incarnates the mechanism of anyon condensation
transition. Our model harbors two topological QSLs in different parameter
regions, a non-abelian Kitaev spin liquid (KSL) bilayer state and a resonating
valence bond (RVB) state. The bilayer-KSL-to-RVB transition indeed occurs by
the mechanism of anyon condensation, which we identify by using parton theories
and exact diagonalization studies. Moreover, we observe "anyon confinement"
phenomena in our numerical results, akin to the quark confinement in high
energy physics. Namely, non-abelian Ising anyons of the bilayer KSL are
confined in the transition to the RVB state. Implications and extensions of
this study are discussed in various aspects such as (i) anyon-condensed
multilayer construction of the Kitaev's sixteenfold way of anyon theories, (ii)
additional vison condensation transition from the RVB to a valence bond solid
(VBS) in the Kitaev bilayer system, (iii) dynamical anyon condensation in a
non-Hermitian Kitaev bilayer, (iv) generalizations of our model to other
lattice geometries, and (v) experimental realizations. This work puts together
the two fascinating QSLs that are extensively studied in modern condensed
matter and quantum physics into a concrete spin model, offering a comprehensive
picture that unifies the anyon physics of the Kitaev spin liquids and the
resonating valence bonds.
