Further Explorations of the Parameter Space of 3D Lattice Gauge Theories
Year: 2015
Type: preprint
Abstract: State sum models 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 from such partition functions by carrying out the state sum construction on a manifold with boundary. The parameter space of these transfer contains various Hamiltonians of physical interest. The 2D quantum double Hamitlonians 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 [12]. 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 is not invariant by translations and thus it is natural to expect to obtain disordered Hamiltonians from the transfer matrices resulting from these constructions. 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.
Source: arXiv (Cornell University)
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2096544185