Abstract
We study the topological phase transitions of a Kitaev chain frustrated by the addition of a single long-range hopping. In order to study the topological properties of the resulting legged-ring geometry (Kitaev tie model), we generalize the transfer matrix approach through which the emergence of Majorana edge modes is analyzed. We find that geometric frustration gives rise to a topological phase diagram in which non-trivial phases alternate with trivial ones at varying the range of the hopping and the chemical potential. Robustness to disorder of non-trivial phases is also proven. Moreover, geometric frustration effects persist when translational invariance is restored by considering a multiple-tie system. These findings shed light on an entire class of experimentally realizable topological systems with long-range couplings.
Highlights
Topological quantum matter and Majorana quasiparticles have attracted growing interest from the scientific community
Once the transfer matrix (TM) is known, the topological phase transitions can be analyzed by imposing the localization requirement of the Majorana modes, which corresponds to the equation aL+1 = T11a1 + T12a0 complemented by the open boundary condition aL+1 = a0 = 0
We have presented an analysis of the topological phase diagram of a Kitaev chain affected by geometric frustration caused by the presence of a long-range hopping (Kitaev tie)
Summary
Topological quantum matter and Majorana quasiparticles have attracted growing interest from the scientific community. In order to study topological frustration effects in a translational-invariant system, we propose a multiple-tie model in which the topological phase transitions can be studied by using the bulk invariant, i.e., the Majorana number. In this context, we demonstrate that topological frustration effects persist even in a translationalinvariant system.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
