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SUMMARY:Imparting the generalised Toric Code with hopping dynamics - Sidda
 rth Vadnerkar (UC Davis)
DTSTART:20230817T130000Z
DTEND:20230817T140000Z
UID:TALK203935@talks.cam.ac.uk
CONTACT:Claudio
DESCRIPTION:The Toric Code is a celebrated toy model that gives us an expl
 icit construction of $\\mathbb{Z}_2$ topological order on a lattice. In th
 is model\, one can create states with anyons\, and move them around using 
 string operators. For all its strengths\, it is still a toy model with a c
 ompletely flat spectrum (the Hamiltonian is made up of commuting projector
 s). There is a generalisation of this model to abelian finite groups $G$\,
  known as the Quantum Double models. This is the class of models we consid
 er in this talk. To make this model more physical\, we introduce a family 
 of perturbations to this Hamiltonian that correspond to anyon hoppings\, i
 n the same spirit as the Hubbard model. These perturbations respect the im
 portant symmetries of the original model. We then solve for the resulting 
 spectrum and find interesting features in it such as a massless generalise
 d Dirac Cone which becomes massive after duality symmetry breaking\, and t
 he creation of a stable bound-pair for a large range of perturbation param
 eters.
LOCATION:TCM Seminar Room
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