Exact solution of Z_2 Chern-Simons model on a triangular lattice

Details Exact solution of Z_2 Chern-Simons model on a triangular lattice Exact solution of Z_2 Chern-Simons model on a triangular lattice

2005-10-23

arxiv.org/abs/cond-mat/0510604v1

Phys. Rev. A 72, 032303 (2005)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 4 figures

Scientific paper

10.1103/PhysRevA.72.032303

We construct the Hamiltonian description of the Chern-Simons theory with Z_n gauge group on a triangular lattice. We show that the Z_2 model can be mapped onto free Majorana fermions and compute the excitation spectrum. In the bulk the spectrum turns out to be gapless but acquires a gap if a magnetic term is added to the Hamiltonian. On a lattice edge one gets additional non-gauge invariant (matter) gapless degrees of freedom whose number grows linearly with the edge length. Therefore, a small hole in the lattice plays the role of a charged particle characterized by a non-trivial projective representation of the gauge group, while a long edge provides a decoherence mechanism for the fluxes. We discuss briefly the implications for the implementations of protected qubits.

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