Gapless Hamiltonians for the Toric Code Using the Projected Entangled Pair State Formalism

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Fernández González, Carlos
Schuch, Norbert
Wolf, Michael M.
Cirac, J.I.
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American Physical Society
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We study Hamiltonians which have Kitaev's toric code as a ground state, and show how to construct a Hamiltonian which shares the ground space of the toric code, but which has gapless excitations with a continuous spectrum in the thermodynamic limit. Our construction is based on the framework of projected entangled pair states, and can be applied to a large class of two-dimensional systems to obtain gapless "uncle Hamiltonians."
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