Gapless Hamiltonians for the toric code using the projected entangled pair state 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, and can be applied to a large class of two-dimensional systems to obtain gapless "uncle Hamiltonians."
Departamento de Física de los Materiales, Universidad Nacional de Educación a Distancia (UNED), 28040 Madrid, Spain.
Carlos
C
Fernández-González
Norbert
N
Schuch
Michael M
MM
Wolf
J Ignacio
JI
Cirac
David
D
Pérez-García