Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2007-12-07
Ann. Phys. 323, 2286 (2008)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
32 pages, 13 figures; corrected typos and changed SU(2)_2 to Ising
Scientific paper
10.1016/j.aop.2007.12.009
The spectral properties of Kitaev's honeycomb lattice model are investigated both analytically and numerically with the focus on the non-abelian phase of the model. After summarizing the fermionization technique which maps spins into free Majorana fermions, we evaluate the spectrum of sparse vortex configurations and derive the interaction between two vortices as a function of their separation. We consider the effect vortices can have on the fermionic spectrum as well as on the phase transition between the abelian and non-abelian phases. We explicitly demonstrate the $2^n$-fold ground state degeneracy in the presence of $2n$ well separated vortices and the lifting of the degeneracy due to their short-range interactions. The calculations are performed on an infinite lattice. In addition to the analytic treatment, a numerical study of finite size systems is performed which is in exact agreement with the theoretical considerations. The general spectral properties of the non-abelian phase are considered for various finite toroidal systems.
Carollo Angelo
Kells Graham
Lahtinen Ville
Pachos Jiannis K.
Stitt Tim
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