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• W2214656275 abstract "A state sum construction on closed manifoldsla Kuperberg can be used to construct the partition functions of 3D lattice gauge theories based on involutory Hopf algebras, A, of which the group algebras, CG, are a particular case. Transfer matrices can be obtained by carrying out this construction on a manifold with boundary. Various Hamiltonians of physical interest can be obtained from these transfer matrices by playing around with the parameters the transfer matrix is a function of. The 2D quantum double Hamiltonians of Kitaev can be obtained from such transfer matrices for specific values of these parameters. A initial study of such models has been carried out in (1). In this paper we study other regions of this parameter space to obtain some new and known models. The new model comprise of Hamiltonians which partially confine the excitations of the quantum double Hamiltonians which are usually deconfined. The state sum construction allows for parameters depending on the position in obtaining the transfer matrices and thus it is natural to expect disordered Hamiltonians from them. Thus one set of known models consist of the disordered quantum double Hamiltonians. Finally we obtain quantum double Hamiltonians perturbed by magnetic fields which have been considered earlier in the literature to study the stability of topological order to perturbations." @default.
• W2214656275 created "2016-06-24" @default.
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• W2214656275 date "2015-04-22" @default.
• W2214656275 modified "2023-09-27" @default.
• W2214656275 title "Toric code-like models from the parameter space of $3D$ lattice gauge theories" @default.
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• W2214656275 hasPublicationYear "2015" @default.
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