WebNov 10, 2024 · The Walker–Wang models are a class of 3-dimensional gapped commuting projector Hamiltonian lattice models with no bulk anyon excitations. When a 2-dimensional surface boundary is introduced, a Walker–Wang model can be terminated at this surface in such a way that it remains a gapped commuting projector model. WebCommuting-projector Hamiltonians comprise a widely studied class of exactly solvable models. As the name sug-gests, these Hamiltonians consist of sums of projectors that commute with each other, so that all energy eigenstates are simultaneous eigenstates of each projector. Classic exam-ples include Kitaev’s quantum-double models [1] and Levin-
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WebFeb 1, 2024 · We present commuting projector Hamiltonian realizations of a large class of (3 + 1)D topological models based on mathematical objects called unitary G-crossed braided fusion categories. This construction comes with a wealth of examples from the literature of symmetry-enriched topological phases. The spacetime counterparts to our … WebWe introduce a family of commuting-projector Hamiltonians whose degrees of freedom involve Z 3 parafermion zero modes residing in a parent fractional-quantum-Hall fluid. The two simplest models in this family emerge from dressing Ising-paramagnet and toric … batch meme
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Webdefine a local commuting projector Hamiltonian H′ such that every ground state of H′ is a ground state of H, so in this paper we focus on the case of local commuting projector Hamiltonians). Note that for a locally commuting projector Hamiltonian, since each hZ is a projector, the operator norm of hZ is bounded by 1 (indeed, the norm WebOne nice feature of a commuting projector Hamiltonian is that all the eigenvalues are integers, so that the issue of a promise gap does not arise: that is, given that the Hamiltonian is a sum of commuting projectors one knows that if the energy is greater than some given E 0 subscript 𝐸 0 E_{0} italic_E start_POSTSUBSCRIPT 0 end ... WebJan 31, 2024 · We also show that for any local commuting projector Hamiltonian, the relative chiral central charge vanishes, while for free fermionic systems, it is related to the zero-temperature electric Hall conductance via the Wiedemann-Franz law. Received 9 October 2024; Revised 14 January 2024; targi uroda gdansk