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Award ID contains: 2108390

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  1. ; (, Communications in Mathematical Physics)
    Abstract We give a complete classification of the anyon sectors of Kitaev’s quantum double model on the infinite triangular lattice and for finite gauge groupG, including the non-abelian case. As conjectured, the anyon sectors of the model correspond precisely to equivalence classes of irreducible representations of the quantum double algebra ofG. 
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  2. ; ; (, Letters in Mathematical Physics)
    Abstract We prove that uniformly small short-range perturbations do not close the bulk gap above the ground state of frustration-free quantum spin systems that satisfy a standard local topological quantum order condition. In contrast with earlier results, we do not require a positive lower bound for finite-system spectral gaps uniform in the system size. To obtain this result, we extend the Bravyi–Hastings–Michalakis strategy so it can be applied to perturbations of the GNS Hamiltonian of the infinite-system ground state. 
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  3. ; ; ; (, arXiv)
    We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge gap dominates the neutral gap. We verify these conditions under a triad of symmetries (translation-invariance, charge and dipole conservation) that are present, e.g., in periodic fractional quantum Hall systems. Thus, this gap domination, previously observed numerically, is a universal feature imposed by symmetry. A second relation yields a new induction-on-particle-number method for deriving spectral gaps. The results cover both bosons and fermions. 
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    Free, publicly-accessible full text available July 24, 2026
  4. ; ; (, Journal of Mathematical Physics)
    We introduce a family of quantum spin Hamiltonians on Z2 that can be regarded as perturbations of Kitaev’s Abelian quantum double models that preserve the gauge and duality symmetries of these models. We analyze in detail the sector with one electric charge and one magnetic flux and show that the spectrum in this sector consists of both bound states and scattering states of Abelian anyons. Concretely, we have defined a family of lattice models in which Abelian anyons arise naturally as finite-size quasi-particles with non-trivial dynamics that consist of a charge-flux pair. In particular, the anyons exhibit a non-trivial holonomy with a quantized phase, consistent with the gauge and duality symmetries of the Hamiltonian. 
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    Full Text Available 
  5. (, EMS Press)
    Frank, Rupert L; Laptev, Ari; Lewin, Mathieu; Seiringer, Robert (Ed.)
    I review the role of Lieb-Robinson bounds in characterizing and utilizing the locality properties of the Heisenberg dynamics of quantum lattice systems. In particular, I discuss two definitions of gapped ground state phases and show that they are essentially equivalent. 
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    Accepted Manuscript Full Text Available