Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations

2007/03/31 by Han-Dong Chen, Zohar Nussinov · 3 citations
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #cond-mat.str-el #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8113/41/7/075001

14 pages, 7 figures

arxiv created 2008/01/17 · arxiv updated 2009/12/01

Abstract

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 type fermionic ground states of this system in terms of the original spins, (ii) adduce that symmetry alone dictates the existence of string and planar brane type correlators and their composites, (iii) compute the value of such non-local correlators by employing the Jordan-Wigner transformation, (iv) affirm that the spectrum is inconsequential to the existence of topological quantum order and that such information is encoded in the states themselves, and (v) express the anyonic character of the excitations in this system and the local symmetries that it harbors in terms of fermions.

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• Band Structure and topology of a periodically deformed Kitaev honeycomb model
• Exact Organization of Density Matrices and Entanglement Structure in the Kitaev Spin Liquid
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers

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