Local interactions and non-Abelian quantum loop gases

Details Local interactions and non-Abelian quantum loop gases Local interactions and non-Abelian quantum loop gases

2008-05-14

arxiv.org/abs/0805.2177v1

Phys. Rev. Lett. 101, 230401 (2008).

Physics

Condensed Matter

Statistical Mechanics

4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.101.230401

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 non-local interactions (or non-trivial inner products). Perturbing a local, gapless Hamiltonian with an anticipated ``non-Abelian'' ground-state wavefunction 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.

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