Abstract:
Kitaev’s lattice models are usually defined as representations of the Drinfeld
quantum double D(H) = H ./H op, as an example of a double cross product quantum
group. We propose a new version based instead on M(H) = Hcop I/H as an example
of Majid’s bicrossproduct quantum group, related by semidualisation or ‘quantum Born
reciprocity’ 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
Hcop I/H. Even though the bicrossproduct has a more complicated and entangled coproduct,
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.
