A $\Gamma$-matrix generalization of the Kitaev model

Abstract

We extend the Kitaev model defined for the Pauli-matrices to the Clifford algebra of $\Gamma$-matrices, taking the $4\times 4$ representation as an example. On a decorated square lattice, the ground state spontaneously breaks time-reversal symmetry and exhibits a topological phase transition. The topologically non-trivial phase carries gapless chiral edge modes along the sample boundary. On the 3D diamond lattice, the ground states can exhibit gapless 3D Dirac cone-like excitations and gapped topological insulating states. Generalizations to even higher rank $\Gamma$-matrices are also discussed.

A revised version

References in corpus (37)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Anyons in an exactly solved model and beyond
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological invariants of time-reversal-invariant band structures
• Quantum Spin Hall Effect
• Quantum orders in an exact soluble model
• Exact results for spin dynamics and fractionization in the Kitaev Model
• The Flux-Phase of the Half-Filled Band
• An exact chiral spin liquid with non-Abelian anyons
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors
• Exact SO(5) Symmetry in spin 3/2 fermionic system
• Exact Quantization of Even-Denominator Fractional Quantum Hall State at $\nu$=5/2 Landau Level Filling Factor
• Insulating and Fractional Quantum Hall States in the N=1 Landau Level
• A Class of $P,T$-Invariant Topological Phases of Interacting Electrons
• Fermions, strings, and gauge fields in lattice spin models
• Exactly solvable Kitaev model in three dimensions
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• Algebraic spin liquid in an exactly solvable spin model
• Quantum order from string-net condensations and origin of light and massless fermions
• Emergent Fermions and Anyons in the Kitaev Model
• Mosaic spin models with topological order
• Creation and Manipulation of Anyons in the Kitaev Model
• Three-dimensional topological phase on the diamond lattice
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid
• An exactly soluble model with tunable p-wave paired fermion ground states
• Topological superfluids with time reversal symmetry
• Explicit demonstration of nonabelian anyon, braiding matrix and fusion rules in the Kitaev-type spin honeycomb lattice models
• Explicit illustration of non-abelian fusion rules in a small spin lattice

Cited by in corpus (58)

• Quantum Spin Liquid States
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• Topological Insulators on the Decorated Honeycomb Lattice
• Exact Chiral Spin Liquid with Stable Spin Fermi Surface on the Kagome Lattice
• SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations
• Majorana Corner Modes in a Second-Order Kitaev Spin Liquid
• Chiral spin-orbital liquids with nodal lines
• Fractional topological phases in three-dimensional coupled-wire systems
• Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Kaleidoscope of topological phases with multiple Majorana species
• Topological Insulators and Quantum Spin Liquids
• Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
• Order Fractionalization in a Kitaev-Kondo model
• An exactly solvable BCS-Hubbard Model in arbitrary dimensions
• SU(2)-invariant Majorana spin liquid with stable parton Fermi surfaces in an exactly solvable model
• Three-dimensional topological phases in a layered honeycomb spin-orbital model
• Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
• An Exact Chiral Amorphous Spin Liquid
• Quintet pairing and non-Abelian vortex string in spin-3/2 cold atomic systems
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Spin-1 Kitaev model in one dimension
• Dynamics of a two-dimensional quantum spin-orbital liquid: spectroscopic signatures of fermionic magnons
• Kitaev spin-orbital bilayers and their moiré superlattices
• Exactly Solvable Topological Chiral Spin Liquid with Random Exchange
• Geometric Criterion for Solvability of Lattice Spin Systems
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• A Kitaev-type spin liquid on a quasicrystal
• Power-Law Behavior of Bond Energy Correlators in a Kitaev-type Model with a Stable Parton Fermi Surface
• Realization of the Exactly Solvable Kitaev Honeycomb Lattice Model in a Spin Rotation Invariant System
• Magnetic fragmentation and fractionalized Goldstone modes in a bilayer quantum spin liquid
• Quadrupolar spin liquid, octupolar Kondo coupling and odd-frequency superconductivity in an exactly solvable model
• $Z_3$ generalization of the Kitaev's spin-1/2 model
• Compass and Kitaev models -- Theory and Physical Motivations
• An exactly solvable dissipative spin liquid
• Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
• Entanglement of a 3D generalization of the Kitaev model on the diamond lattice
• Hyperbolic Spin Liquids
• Bosonization of Majorana modes and edge states
• Pristine Mott Insulator from an Exactly Solvable Spin-1/2 Kitaev Model
• Partial flux ordering and thermal Majorana metals in (higher-order) spin liquids
• Exactly solvable model of topological insulator realized on spin-1/2 lattice
• Projective symmetry group classification of $Z_3$ parafermion spin liquids on a honeycomb lattice
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Quasicrystalline Spin Liquid
• Magnetic order through Kondo coupling to quantum spin liquids
• Majorana corner states in square and Kagome quantum spin liquids
• A study of dissipative models based on Dirac matrices
• Floating topological phases
• Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way
• Exactly Solvable 1D Quantum Models with Gamma Matrices
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Three-dimensional spin-orbital liquids
• Emergent spacetime supersymmetry at 2D fractionalized quantum criticality
• Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices
• Giant magnetoresistance of edge current between fermion and spin topological systems