Time-reversal symmetric Kitaev model and topological superconductor in two dimensions

Abstract

A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z_2 gauge fields. The Majorana fermion model can be viewed as a model of time-reversal invariant superconductor and is classified as a member of symmetry class DIII in the Altland-Zirnbauer classification. The ground-state phase diagram has two topologically distinct gapped phases which are distinguished by a Z_2 topological invariant. The topologically nontrivial phase supports both a Kramers' pair of gapless Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana states bound to a 0-flux vortex in the π-flux background. Power-law decaying correlation functions of spins along the edge are obtained by taking the gapless Majorana edge modes into account. The model is also defined on the one-dimension ladder, in which case again the ground-state phase diagram has Z_2 trivial and non-trivial phases.

17 pages, 9 figures

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Cited by in corpus (21)

• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Fractionalized fermionic quantum criticality in spin-orbital Mott insulators
• Majorana Corner Modes in a Second-Order Kitaev Spin Liquid
• Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Lieb-Schultz-Mattis theorems for symmetry protected topological phases
• An exactly solvable BCS-Hubbard Model in arbitrary dimensions
• Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
• Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions
• A Kitaev-type spin liquid on a quasicrystal
• Magnetic fragmentation and fractionalized Goldstone modes in a bilayer quantum spin liquid
• Compass and Kitaev models -- Theory and Physical Motivations
• Phase diagrams of SO($N$) Majorana-Hubbard models: Dimerization, internal symmetry breaking, and fluctuation-induced first-order transitions
• Spin Transport in Quantum Spin-Orbital Liquids
• Entanglement of a 3D generalization of the Kitaev model on the diamond lattice
• Pristine Mott Insulator from an Exactly Solvable Spin-1/2 Kitaev Model
• Magnetic order through Kondo coupling to quantum spin liquids
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Hidden chiral symmetries in BDI multichannel Kitaev chains
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices
• Three-dimensional spin-orbital liquids