Gapless Hamiltonians for the toric code using the PEPS formalism
  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 "uncle Hamiltonians". 
Carlos Fern\'andez-Gonz\'alez, Norbert Schuch, Michael M. Wolf, J.   Ignacio Cirac and David P\'erez-Garc\'ia
quant-ph cond-mat.str-el