Dresden 2020 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 73: Topology: Other Topics

TT 73.5: Vortrag

Freitag, 20. März 2020, 12:00–12:15, HSZ 103

Parafermions and Z3 Charge-Flux attachment — •Peng Rao and Inti Sodemann — Max Planck Institute for the Physics of Complex System, Dresden

A recent construction (Ann. Phys. 393, 234 (2018)) has introduced an interesting route to bosonization of fermions in two spatial dimensions by implementing a precise lattice version of flux-charge binding. The idea is to modify Kitaev’s Toric code so that the electric charge (e) and magnetic flux (m) are always created in a tight “dipolar" pair ε (=e × m) which is a fermion, providing a way to represent any local fermionic Hamiltonian as a local Hamiltonian of spins. We discuss an extension of these ideas to the case of a ZN toric code which allows a bosonization of anyons with more general statistical angles. We have focused particularly in the case of N=3. We will prove that ground states in the torus in this case are at least three-fold degenerate, and, discuss a model featuring a topological phase transition between a 3-fold degenerate state and a 9-fold degenerate ground state featuring parafermionic excitations.

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