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Quantum Thermodynamics

Emergent Fermions and Anyons in the Kitaev Model

arXiv
Authors: K. P. Schmidt, S. Dusuel, J. Vidal

Year

2007

Paper ID

49032

Status

Preprint

Abstract Read

~2 min

Abstract Words

108

Citations

N/A

Abstract

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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  • This paper contributes to the Quantum Thermodynamics research area in the Quantum Articles archive.
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  • We study the gapped phase of the Kitaev model on the honeycomb lattice using perturbative continuous unitary transformations.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0709.3017 [2] arXiv https://arxiv.org/abs/0709.3017 [3] Publisher https://arxiv.org/abs/0709.3017

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