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arXiv · 1701.04456

Anyons are not energy eigenspaces of quantum double Hamiltonians

Anna Komar·Olivier Landon-Cardinal
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Abstract

Kitaev's quantum double models, including the toric code, are canonical examples of quantum topological models on a 2D spin lattice. Their Hamiltonian defines the groundspace by imposing an energy penalty to any nontrivial flux or charge, but does not distinguish among those. We generalize this construction by introducing a novel family of Hamiltonians made of commuting four-body projectors that provide an intricate splitting of the Hilbert space by discriminating among non-trivial charges and fluxes. Our construction highlights that anyons are not in one-to-one correspondence with energy eigenspaces, a feature already present in Kitaev's construction. This discrepancy is due to the presence of local degrees of freedom in addition to topological ones on a lattice.

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Anna Komar, Olivier Landon-Cardinal. 2017-09-07. Anyons are not energy eigenspaces of quantum double Hamiltonians. https://doi.org/10.1103/physrevb.96.195150

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