Anyon condensation and confinement transition in a Kitaev spin liquid bilayer

TL;DR

This paper introduces a concrete spin model demonstrating anyon condensation and confinement transitions between two quantum spin liquids, providing insights into topological order changes and potential experimental realizations.

Contribution

It presents a specific spin model that confirms the mechanism of anyon condensation transition between non-abelian Kitaev spin liquids and RVB states, supported by theoretical and numerical analysis.

Findings

Confirmed anyon condensation transition between KSL and RVB states

Observed anyon confinement phenomena similar to quark confinement

Identified non-abelian Ising anyons confinement during transition

Abstract

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.