An Exact Chiral Amorphous Spin Liquid

Abstract

Topological insulator phases of non-interacting particles have been generalized from periodic crystals to amorphous lattices, which raises the question whether topologically ordered quantum many-body phases may similarly exist in amorphous systems? Here we construct a soluble chiral amorphous quantum spin liquid by extending the Kitaev honeycomb model to random lattices with fixed coordination number three. The model retains its exact solubility but the presence of plaquettes with an odd number of sides leads to a spontaneous breaking of time reversal symmetry. We unearth a rich phase diagram displaying Abelian as well as a non-Abelian quantum spin liquid phases with a remarkably simple ground state flux pattern. Furthermore, we show that the system undergoes a finite-temperature phase transition to a conducting thermal metal state and discuss possible experimental realisations.

5 pages, 3 figures

References in corpus (15)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Models and Materials for Generalized Kitaev Magnetism
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Designer disordered materials with large complete photonic band gaps
• Exact results for spin dynamics and fractionization in the Kitaev Model
• An exact chiral spin liquid with non-Abelian anyons
• A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
• Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for honeycomb lattice iridates A2IrO3
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Weyl spin liquids
• Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR lineshape
• A $\Gamma$-matrix generalization of the Kitaev model
• Toward Realistic Amorphous Topological Insulators
• Quantised Bulk Conductivity as a Local Chern Marker
• Fractionalization and topology in amorphous electronic solids

Cited by in corpus (15)

• Kitaev Quantum Spin Liquids
• Amorphous quantum magnets in a two-dimensional Rydberg atom array
• Kitaev-Heisenberg model on the star lattice: From chiral Majorana fermions to chiral triplons
• Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid
• Hyperbolic Spin Liquids
• Chiral Gapless Spin Liquid in Hyperbolic Space
• Structure-driven phase transitions in paracrystalline topological insulators
• Kitaev model in regular hyperbolic tilings
• Observation of average topological phase in disordered Rydberg atom array
• A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system
• Quasicrystalline Spin Liquid
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Effective models for dense vortex lattices in the Kitaev honeycomb model
• Genuine topological Anderson insulator from impurity induced chirality reversal
• Real-space chirality from crystalline topological defects in the Kitaev spin liquid