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Gapless Hamiltonians for the toric code using the PEPS formalism

Carlos Fernández-González, Norbert Schuch, Michael M. Wolf, J. Ignacio Cirac, David Pérez-García

Phys. Rev. Lett. 109, 260401 , (2012) 1111.5817 Pfeil

Abstract: 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 (PEPS), and can be applied to a large class of two-dimensional systems to obtain gapless