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TT: Fachverband Tiefe Temperaturen
TT 1: Topology: Majorana Physics
TT 1.4: Vortrag
Montag, 5. September 2022, 10:30–10:45, H10
Edge Z3 parafermions in fermionic lattices. — •Raphael L R C Teixeira1,2 and Luis G G V Dias da Silva1 — 1Instituto de Fisica - Universidade de Sao Paulo, Sao Paulo Brazil — 2Department of Physics and Materials Science Université du Luxembourg, Luxembourg, Luxembourg
Parafermions modes are non-Abelian anyons which were introduced as ZN generalizations of Z2 Majorana states. In particular, Z3 parafermions can be used to produce Fibonacci anyons, laying a path towards universal topological quantum computation. Due to their fractional nature, much of theoretical work on Z3 parafermions has relied on bosonization methods or parafermionic operators. In this work, we introduce a representation of Z3 parafermions in terms of purely fermionic models operators in the single-occupancy basis (t−J regime). We establish the equivalency of a family of 1D-lattice fermionic models written in the t−J model basis supporting free Z3 parafermonic modes at its ends. By using density matrix renormalization group calculations, we are able to characterize the topological phase transition and study the effect of local operators (doping and magnetic fields) on the spatial localization of the parafermionic modes and their stability. Moreover, we discuss the necessary ingredients towards realizing Z3 parafermions in strongly interacting electronic systems.