Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2004-10-27
Phys. Rev. B 71, 184424 (2005)
Physics
Condensed Matter
Strongly Correlated Electrons
11 pages, 7 (.eps) figures. Improved discussion of the destruction of the topological degeneracy and other minor corrections.
Scientific paper
10.1103/PhysRevB.71.184424
We consider a quantum dimer model (QDM) on the kagome lattice which was introduced recently [Phys. Rev. Lett. 89, 137202 (2002)]. It realizes a Z_2 liquid phase and its spectrum was obtained exactly. It displays a topological degeneracy when the lattice has a non-trivial geometry (cylinder, torus, etc). We discuss and solve two extensions of the model where perturbations along lines are introduced: first the introduction of a potential energy term repelling (or attracting) the dimers along a line is added, second a perturbation allowing to create, move or destroy monomers. For each of these perturbations we show that there exists a critical value above which, in the thermodynamic limit, the degeneracy of the ground-state is lifted from 2 (on a cylinder) to 1. In both cases the exact value of the gap between the first two levels is obtained by a mapping to an Ising chain in transverse field. This model provides an example of solvable Hamiltonian for a topological quantum bit where the two perturbations act as a diagonal and a transverse operator in the two-dimensional subspace. We discuss how crossing the transitions may be used in the manipulation of the quantum bit to optimize simultaneously the frequency of operation and the losses due to decoherence.
Lhuillier Claire
Mila Frédéric
Misguich Grégoire
Pasquier Vincent
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