Anyon condensation and confinement transition in a Kitaev spin liquid bilayer

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.

21 pages, 13 figures, 3 tables

References in corpus (42)

• Non-Abelian Anyons and Topological Quantum Computation
• Suppressing quantum errors by scaling a surface code logical qubit
• Logical quantum processor based on reconfigurable atom arrays
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Identifying Topological Order by Entanglement Entropy
• Interactions and phase transitions on graphene's honeycomb lattice
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• An exact chiral spin liquid with non-Abelian anyons
• Condensate induced transitions between topologically ordered phases
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Quantum phases of Rydberg atoms on a kagome lattice
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• A short introduction to Fibonacci anyon models
• Quantum criticality under decoherence or weak measurement
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Theory of the field-revealed Kitaev spin liquid
• Digital simulation of non-Abelian anyons with 68 programmable superconducting qubits
• Shortest Route to Non-Abelian Topological Order on a Quantum Processor
• Measurements conspire nonlocally to restructure critical quantum states
• Constraints on topological order in Mott Insulators
• Anyon condensation and the color code
• Engineering and probing non-Abelian chiral spin liquids using periodically driven ultracold atoms
• Non-Abelian Floquet Spin Liquids in a Digital Rydberg Simulator
• Pauli stabilizer models of twisted quantum doubles
• Triangular lattice quantum dimer model with variable dimer density
• Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model
• Generalized Hardcore Dimer Models approach to low-energy Heisenberg frustrated antiferromagnets: general properties and application to the kagome antiferromagnet
• Quantum Dimer Model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Crystallization of the resonating valence bond liquid as vortex condensation
• Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model
• Non-Abelian statistics with mixed-boundary punctures on the toric code
• Quantum phase transitions in the $K$-layer Ising toric code
• Equivalence between vortices, twists and chiral gauge fields in Kitaev's honeycomb lattice model
• Edge Theories for Anyon Condensation Phase Transitions
• Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way

Cited by in corpus (6)

• Gauge Field Dynamics in Multilayer Kitaev Spin Liquids
• Dualities between 2+1d fusion surface models from braided fusion categories
• Mixed-State Quantum Spin Liquids and Dynamical Anyon Condensations in Kitaev Lindbladians
• Kitaev Meets Affleck-Kennedy-Lieb-Tasaki: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems
• Topology-driven deconfined quantum criticality in magnetic bilayers
• Vison condensation and spinon confinement in a kagome-lattice ${\mathbb{Z}}_2$ spin liquid: A numerical study of a quantum dimer model