Anyons in an exactly solved model and beyond

  title={Anyons in an exactly solved model and beyond},
  author={Alexei Y. Kitaev},
  journal={Annals of Physics},
  • A. Kitaev
  • Published 17 June 2005
  • Physics
  • Annals of Physics
Signatures of non-Abelian anyons in the thermodynamics of an interacting fermion model
The contribution of anyonic degrees of freedom emerging in the non-Abelian spin sector of a one-dimensional system of interacting fermions carrying both $SU(2)$ spin and $SU(N_f)$ orbital degrees of
Topological edge states in a one-dimensional ladder system
In this thesis, an interacting, particle number conserving model of spinless fermions in a two-leg ladder system is analyzed in the context of topological edge states. As proven in [1], where the
Topological phases in two-dimensional arrays of parafermionic zero modes
It has recently been realized that zero modes with projective non-Abelian statistics, generalizing the notion of Majorana bound states, may exist at the interface between a superconductor and a
Rigorous calculations of non-Abelian statistics in the Kitaev honeycomb model
We develop a rigorous and highly accurate technique for the calculation of the Berry phase in systems with a quadratic Hamiltonian within the context of the Kitaev honeycomb lattice model. The method
Localized Majorana-Like Modes in a Number-Conserving Setting: An Exactly Solvable Model.
A model of interacting fermions in a two-wire geometry supporting nonlocal zero-energy Majorana-like edge excitations has an exactly solvable line, described by a topologically nontrivial ground state wave function.
Odd-frequency pair density wave in the Kitaev-Kondo lattice model
We investigate the properties of the Kitaev-Kondo lattice model defined on a bilayer honeycomb lattice by means of the SO(3) Majorana representation for spin-1/2 moments. We first consider the
Exact results of the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
In this work, we illustrate how a Jordan?Wigner transformation combined with symmetry considerations enables a direct solution of Kitaev's model on the honeycomb lattice. We (i) express the p-wave
Model of spin liquids with and without time-reversal symmetry
We study a model in (2+1)-dimensional spacetime that is realized by an array of chains, each of which realizes relativistic Majorana fields in (1+1)-dimensional spacetime, coupled via current-current


Non-Abelian topological phases in an extended Hubbard model
We describe four closely related Hubbard-like models (models A, B, C and D) of particles that can hop on a 2D Kagome lattice interacting via Coulomb repulsion. The particles can be either bosons
Unpaired Majorana fermions in quantum wires
Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length L possesses
Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
The Pfaffian quantum Hall states, which can be viewed as involving pairing either of spin-polarized electrons or of composite fermions, are generalized by finding the exact ground states of certain
A Magnetic Model with a Possible Chern-Simons Phase
Abstract: An elementary family of local Hamiltonians , is described for a 2-dimensional quantum mechanical system of spin particles. On the torus, the ground state space Gŝ,ℓ is (log) extensively
Discrete non-Abelian gauge theories in two-dimensional lattices and their realizations in Josephson-junction arrays
We discuss real-space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We construct the Hamiltonian formalism which is appropriate for their solid-state physics
Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation
We discuss real-space lattice models equivalent to gauge theories with a discrete non-Abelian gauge group. We construct the Hamiltonian formalism which is appropriate for their solid-state physics
Flux phase of the half-filled band.
  • Lieb
  • Physics
    Physical review letters
  • 1994
The conjecture is verified that the optimum, energy minimizing, magnetic flux for a half-filled band of electrons hopping on a planar, bipartite graph is π per square plaquette. We require only that