Local interactions and non-abelian quantum loop gases.
Two-dimensional quantum loop gases are elementary examples of topological ground states with Abelian or non-Abelian anyonic excitations. While Abelian loop gases appear as ground states of local, gapped Hamiltonians such as the toric code, we show that gapped non-Abelian loop gases require nonlocal interactions (or nontrivial inner products). Perturbing a local, gapless Hamiltonian with an anticipated "non-Abelian" ground-state wave function immediately drives the system into the Abelian phase, as can be seen by measuring the Hausdorff dimension of loops. Local quantum critical behavior is found in a loop gas in which all equal-time correlations of local operators decay exponentially.
Troyer
Matthias
M
Theoretische Physik, Eidgenössische Technische Hochschule Zürich, 8093 Zürich, Switzerland.
Trebst
Simon
S
Shtengel
Kirill
K
Nayak
Chetan
C