QUROPE Quantum Information Processing and Communication in Europe

We show that Projected Entangled-Pair States (PEPS) in two spatial dimensions can describe chiral topological states by explicitly constructing a family of such states with a non-trivial Chern number. They are ground states of two different kinds of free-fermion Hamiltonians: (i) local and gapless; (ii) gapped, but with hopping amplitudes that decay according to a power law. We also prove that they are necessarily non-injective, and cannot correspond to exact ground states of gapped, local parent Hamiltonians. We provide numerical evidence that they can nevertheless approximate well the physical properties of topological insulators with local Hamiltonians at arbitrary temperatures.