Abstract
Already Kitaev’s original paper (Kitaev 2006) introducing the honeycomb lattice model is mainly concerned with an extended version of the Hamiltonian, Eq. (2.1), which gives rise to excitations with non-Abelian statistics. These quasiparticles play a central role in topological quantum computation due to their inherent stability against local perturbations that could lead to decoherence, for a review see Nayak et al. (2008). In this thesis I am mainly interested in the spin liquid properties. Thus, the objective of this chapter is to calculate the spin excitations in such an exactly solvable non-Abelian spin liquid and to search for salient signatures of the phase in the structure factor.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
G. Baskaran, S. Mandal, R. Shankar, Exact results for spin dynamics and fractionalization in the Kitaev model. Phys. Rev. Lett. 98(24), 247201 (2007)
J.T. Chalker, N. Read, V. Kagalovsky, B. Horovitz, Y. Avishai, A.W.W. Ludwig, Thermal metal in network models of a disordered two-dimensional superconductor. Phys. Rev. B 65(1), 012506 (2001)
M. Cheng, R.M. Lutchyn, V. Galitski, S. Das Sarma, Splitting of Majorana-Fermion modes due to intervortex tunneling in a p x + ip y superconductor. Phys. Rev. Lett. 103(10), 107001 (2009)
V. Chua, G.A. Fiete, Exactly solvable topological chiral spin liquid with random exchange. Phys. Rev. B 84(19), 195129 (2011)
X.-Y. Feng, G.-M. Zhang, T. Xiang, Topological characterization of quantum phase transitions in a spin-model. Phys. Rev. Lett. 98(8), 087204 (2007)
D.A. Ivanov, Non-Abelian statistics of half-quantum vortices in p-wave superconductors. Phys. Rev. Lett. 86(2), 268–271 (2001)
A. Kitaev, Anyons in an exactly solved model and beyond. Ann. Phys. 321(1), 2–111 (2006)
Y.E. Kraus, A. Stern, Majorana fermions on a disordered triangular lattice. New J. Phys. 13(10), 105006 (2011)
V. Lahtinen, Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model. New J. Phys. 13(7), 075009 (2011)
V. Lahtinen, A.W.W. Ludwig, S. Trebst, Perturbed vortex lattices and the stability of nucleated topological phases. Phys. Rev. B 89(8), 085121 (2014)
C.R. Laumann, A.W.W. Ludwig, D.A. Huse, S. Trebst, Disorder-induced Majorana metal in interacting non-Abelian anyon systems. Phys. Rev. B 85(16), 161301 (2012)
E.H. Lieb, Flux phase of the half-filled band. Phys. Rev. Lett. 73(16), 2158–2161 (1994)
T.A. Loring, M.B. Hastings, Disordered topological insulators via C * -algebras. Europhys. Lett. 92(6), 67004 (2010)
C. Nayak, S.H. Simon, A. Stern, M. Freedman, S. Das Sarma, Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80(3), 1083–1159 (2008)
S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 2001)
X.-F. Shi, Y. Yu, J.Q. You, F. Nori, Topological quantum phase transition in the extended Kitaev spin model. Phys. Rev. B 79(13), 134431 (2009)
M. Vojta, Quantum phase transitions. Rep. Prog. Phys. 66(12), 2069 (2003)
F.J. Wegner, Duality in generalized ising models and phase transitions without local order parameters. J. Math. Phys. 12(10), 2259–2272 (1971)
H. Yao, S.A. Kivelson, Exact chiral spin liquid with non-Abelian anyons. Phys. Rev. Lett 99(24), 247203 (2007)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Knolle, J. (2016). Non-Abelian Phase and the Effect of Disorder. In: Dynamics of a Quantum Spin Liquid. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-23953-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-23953-8_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23951-4
Online ISBN: 978-3-319-23953-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)