Emergent Fermions and Anyons in the Kitaev Model

Details Emergent Fermions and Anyons in the Kitaev Model Emergent Fermions and Anyons in the Kitaev Model

2007-09-19

arxiv.org/abs/0709.3017v2

Phys. Rev. Lett. 100, 057208 (2008)

Physics

Condensed Matter

Other Condensed Matter

4 pages, 5 figures, published version

Scientific paper

10.1103/PhysRevLett.100.057208

We study the gapped phase of the Kitaev model on the honeycomb lattice using perturbative continuous unitary transformations. The effective low-energy Hamiltonian is found to be an extended toric code with interacting anyons. High-energy excitations are emerging free fermions which are composed of hardcore bosons with an attached string of spin operators. The excitation spectrum is mapped onto that of a single particle hopping on a square lattice in a magnetic field. We also illustrate how to compute correlation functions in this framework. The present approach yields analytical perturbative results in the thermodynamical limit without using the Majorana or the Jordan-Wigner fermionization initially proposed to solve this problem.

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