Gapless Hamiltonians for the toric code using the PEPS formalism

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 "uncle Hamiltonians".

8 pages, 2 figures

References in corpus (3)

• Criticality, the area law, and the computational power of PEPS
• Valence Bond Solids for Quantum Computation
• Entropy and Entanglement in Quantum Ground States

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