QN Seminar - Fabian Hassler (Aachen University): 'Topological order and phase transitions in the Majorana toric code'



16:00 hrs


Lectureroom G, Lorentzweg 1, Delft


The toric code based on Majorana fermions on mesoscopic superconducting islands is a promising candidate for quantum information processing. In the limit of vanishing Cooper-pair tunneling, it has been argued that the phase transition separating the topologically ordered phase of the toric code from the trivial one is in the universality class of (2+1)D-XY. On the other hand, in the limit of infinitely large Cooper-pair tunneling, the phase transition is in the universality class of (2+1)D-Ising. We treat the case of finite Cooper-pair tunneling and address the question of how the continuous XY symmetry breaking phase transition turns into a discrete Z2-symmetry breaking one when the Cooper-pair tunneling rate is increased. We show that this happens through a couple of tricritical points and first order phase transitions.