Exact solution of the Z2 Chern-Simons model on a triangular lattice
Abstract
We construct the Hamiltonian description of the Chern-Simons theory with Zn gauge group on a triangular lattice. We show that the Z2 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 nongauge 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 nontrivial 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.
- Publication:
-
Physical Review A
- Pub Date:
- September 2005
- DOI:
- 10.1103/PhysRevA.72.032303
- arXiv:
- arXiv:cond-mat/0510604
- Bibcode:
- 2005PhRvA..72c2303D
- Keywords:
-
- 03.67.Lx;
- 11.15.-q;
- 05.30.Pr;
- Quantum computation;
- Gauge field theories;
- Fractional statistics systems;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 7 pages, 4 figures