Chiral spin liquids with crystalline ${\mathbb{Z}}_2$ gauge order in a three-dimensional Kitaev model

Abstract

Chiral spin liquids (CSLs) are time-reversal symmetry breaking ground states of frustrated quantum magnets that show no long-range magnetic ordering, but instead exhibit topological order and fractional excitations. Their realization in simple and tractable microscopic models has, however, remained an open challenge for almost two decades until it was realized that Kitaev models on lattices with odd-length loops are natural hosts for such states, even in the absence of a time-reversal symmetry breaking magnetic field. Here we report on the formation of CSLs in a three-dimensional Kitaev model, which differ from their widely studied two-dimensional counterparts, namely, they exhibit a crystalline ordering of the ${\mathbb{Z}}_2$ gauge fluxes and thereby break some of the underlying lattice symmetries. We study the formation of these unconventional CSLs via extensive quantum Monte Carlo simulations and demonstrate that they are separated from the featureless paramagnet at high temperatures by a single first-order transition at which both time-reversal and lattice symmetries are simultaneously broken. Using variational approaches for the ground state, we explore the effect of varying the Kitaev couplings and find at least five distinct CSL phases, all of which possess crystalline ordering of the ${\mathbb{Z}}_2$ gauge fluxes. For some of these phases, the complementary itinerant Majorana fermions exhibit gapless band structures with topological features such as Weyl nodes or nodal lines in the bulk and Fermi arc or drumhead surface states.

References in corpus (47)

• Anyons in an exactly solved model and beyond
• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Quantum Spin Liquids
• Topological nodal semimetals
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• The Kernel Polynomial Method
• Quantum Orders and Symmetric Spin Liquids
• Topological nodal line semimetals with and without spin-orbital coupling
• Dirac Line Nodes in Inversion Symmetric Crystals
• Spin-lattice coupling in frustrated antiferromagnets
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• An exact chiral spin liquid with non-Abelian anyons
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Line of Dirac Nodes in Hyper-Honeycomb Lattices
• Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
• Feedback-optimized parallel tempering Monte Carlo
• Emergent Chiral Spin Liquid: Fractional Quantum Hall Effect in a Kagome Heisenberg Model
• Thermal fractionalization of quantum spins in a Kitaev model: $T$-linear specific heat and coherent transport of Majorana fermions
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Vaporization of Kitaev spin liquids
• Exactly solvable Kitaev model in three dimensions
• Protected boundary states in gapless topological phases
• The kagome antiferromagnet: a chiral topological spin liquid ?
• Topological Classification and Stability of Fermi Surfaces
• Classification of gapless Z2 spin liquids in three-dimensional Kitaev models
• Tunable Line Node Semimetals
• Three dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
• Weyl spin liquids
• Rank-finiteness for modular categories
• Majorana Corner Modes in a Second-Order Kitaev Spin Liquid
• Dirac semimetals $A_{3}Bi$ ($A$=Na,K,Rb) as $Z_2$ Weyl semimetals
• Finite-Temperature Phase Transition to a Quantum Spin Liquid in a Three-Dimensional Kitaev Model on a Hyperhoneycomb Lattice
• Thermodynamics of Chiral Spin Liquids with Abelian and Non-Abelian Anyons
• Crystalline Kitaev spin liquids
• Surface Fermi arcs in $Z_2$ Weyl semimetals $A_{3}Bi$ (A=Na, K, Rb)
• Finite-temperature phase transition to a Kitaev spin liquid phase on a hyperoctagon lattice: A large-scale quantum Monte Carlo study
• Green-Function-Based Monte Carlo Method for Classical Fields Coupled to Fermions
• Thermodynamics of a gauge-frustrated Kitaev spin liquid
• Chiral Spin Liquids at Finite Temperature in a Three-Dimensional Kitaev Model
• Topological semimetals and insulators in three-dimensional honeycomb materials
• Topological Crystalline Metal in Orthorhombic Perovskite Iridates
• Global constraints on $Z_2$ fluxes in two different anisotropic limits of a hypernonagon Kitaev model

Cited by in corpus (8)

• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Eight-color chiral spin liquid in the $S=1$ bilinear-biquadratic model with Kitaev interactions
• Ground-State Phase Diagram of the Kitaev-Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice
• Chiral Gapless Spin Liquid in Hyperbolic Space
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
• A quantum Monte Carlo method on asymptotic Lefschetz thimbles for quantum spin systems: An application to the Kitaev model in a magnetic field
• Three-dimensional spin-orbital liquids
• Theory of collective topologically-protected Majorana fermion excitations of networks of localized Majorana modes