A Kitaev-type spin liquid on a quasicrystal

Abstract

We develop an exactly solvable model with Kitaev-type interactions and study its phase diagram on the dual lattice of the quasicrystalline Ammann-Beenker lattice. Our construction is based on the $\Gamma$-matrix generalization of the Kitaev model and utilizes the cut-and-project correspondence between the four-dimensional simple cubic lattice and the Ammann-Beenker lattice to designate four types of bonds. We obtain a rich phase diagram with gapped (chiral and abelian) and gapless spin liquid phases via Monte Carlo simulations and variational analysis. We show that the ground state can be further tuned by the inclusion of an onsite term that selects 21 different vison configurations while maintaining the integrability of the model. Our results highlight the rich physics at the intersection of quasicrystals and quantum magnetism.

References in corpus (8)

• An exact chiral spin liquid with non-Abelian anyons
• Experimental identification of quantum spin liquids
• Quantum critical state in a magnetic quasicrystal
• Imaging Quasi-Periodic Electronic States in a Synthetic Penrose Tiling
• A $\Gamma$-matrix generalization of the Kitaev model
• Antiferromagnetic order in the Hubbard Model on the Penrose Lattice
• Topological states in quasicrystals
• Projective symmetry of partons in Kitaev's honeycomb model

Cited by in corpus (9)

• Nematic Superconductivity and Its Critical Vestigial Phases in the Quasi-crystal
• Topological and magnetic phase transitions in the bilayer Kitaev-Ising model
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Magnetic order through Kondo coupling to quantum spin liquids
• Fractionalized fermionic multicriticality in anisotropic Kitaev spin-orbital liquids
• Quasicrystalline Spin Liquid
• Mott transition and correlation effects on strictly localized states in an octagonal quasicrystal
• Site-selective correlations in interacting "flat-band" quasicrystals
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices