Chiral Spin Liquids at Finite Temperature in a Three-Dimensional Kitaev Model

Abstract

Chiral spin liquids (CSLs) in three dimensions and thermal phase transitions to paramagnet are studied by unbiased Monte Carlo simulations. For an extension of the Kitaev model to a three-dimensional tricoordinate network dubbed the hypernonagon lattice, we derive low-energy effective models in two different anisotropic limits. We show that the effective interactions between the emergent $Z_2$ degrees of freedom called fluxes are unfrustrated in one limit, while highly frustrated in the other. In both cases, we find a first-order phase transition to the CSL, where both time-reversal and parity symmetries are spontaneously broken. In the frustrated case, however, the CSL state is highly exotic --- the flux configuration is subextensively degenerate while showing a directional order with broken $C_3$ rotational symmetry. Our results provide two contrasting archetypes of CSLs in three dimensions, both of which allow approximation-free simulation for the thermodynamics.

8 pages, 7 figures

References in corpus (10)

• Non-Abelian Anyons and Topological Quantum Computation
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• An exact chiral spin liquid with non-Abelian anyons
• Vaporization of Kitaev spin liquids
• Topological order in a 3D toric code at finite temperature
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Interplay of quantum and thermal fluctuations in a frustrated magnet
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• String Picture of a Frustrated Quantum Magnet and Dimer Model
• Global constraints on $Z_2$ fluxes in two different anisotropic limits of a hypernonagon Kitaev model

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• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Thermodynamics of a gauge-frustrated Kitaev spin liquid
• Chiral spin liquids with crystalline ${\mathbb{Z}}_2$ gauge order in a three-dimensional Kitaev model
• Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice
• Projective-symmetry-group analysis of inelastic light scattering in Kitaev spin balls
• Global constraints on $Z_2$ fluxes in two different anisotropic limits of a hypernonagon Kitaev model