Semidual Kitaev lattice model and tensor network representation - Prince Osei

Kitaev’s lattice models were originally proposed to exploit topological phases of matter for fault-tolerant quantum computation. They are usually defined as representations of the Drinfeld quantum double D(H), of a Hopf algebra H. In this talk, I discuss a new version based instead on M(H) a bicrossproduct quantum group, related by semidualisation to D(H). Given a finite-dimensional Hopf algebra H , we show that a quadrangulated oriented surface defines a representation of the bicrossproduct quantum group . The construction of this new model is relatively natural as it relies on the use of the covariant Hopf algebra actions. Working locally, we obtain an exactly solvable Hamiltonian for the model and provide a definition of the ground state in terms of a tensor network representation. Details may be found in