A hierarchy of topological tensor network states

O. BUERSCHAPER, M. CHRISTANDL, M. AGUADO AND M. MOMBELLI

JOURNAL OF MATHEMATICAL PHYSICS

AMER INST PHYSICS

Lugar: New York; Año: 2013 vol. 54

0022-2488

We present a hierarchy of quantum many-body states among which many examples of topological order can be identied by construction. We de- ne these states in terms of a general, basis-independent framework of tensor networks based on the algebraic setting of nite-dimensional Hopf C  -algebras. At the top of the hierarchy we identify ground states of new topological lat- tice models extending Kitaev´s quantum double models [26]. For these states we exhibit the mechanism responsible for their non-zero topological entanglement entropy by constructing a renormalization group ow. Furthermore it is shown that those states of the hierarchy associated with Kitaev´s original quantum dou- ble models are related to each other by the condensation of topological charges. We conjecture that charge condensation is the physical mechanism underlying the hierarchy in general.