Anyons are not energy eigenspaces of quantum double Hamiltonians

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.

18 pages, 8 figures. Added Sec.V and Fig. 7 to clarify "charge flavors"; modififed title

References in corpus (6)

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Cited by in corpus (8)

• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Finite-temperature properties of string-net models
• Excitations in the Higher Lattice Gauge Theory Model for Topological Phases III: the (3+1)-Dimensional Case
• Extended string-net models with all anyons at finite temperature
• Topological phase diagram of $\mathcal{D}(S_3)$ induced by forbidding charges and fluxes
• Finite-group gauge theories on lattices as Hamiltonian systems with constraints
• Partition function of the Kitaev quantum double model