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2D quantum double models from a 3D perspective. (English) Zbl 1300.37048

The paper deals with three dimensional (3D) lattice models considered as the generalizations of the approach used to define the Kuperberg invariant of 3-manifolds. Firstly, one recalls the 3D-model and its relations with lattice gauge theories. Then, one obtains the transfer matrix and one shows how to derive the Hamiltonian from the transfer matrix. The ground states of these models are studied. The model proposed herein provides a uniform approach to various models which are available in the literature.

MSC:

37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems
81P68 Quantum computation
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
94A60 Cryptography
81T25 Quantum field theory on lattices
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