Regensburg 2019 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 11: Majorana Physics
TT 11.11: Talk
Monday, April 1, 2019, 18:00–18:15, H4
Topological Ordering in the Majorana Toric Code — •Alexander Ziesen1, Fabian Hassler1, and Ananda Roy1,2 — 1JARA Institute for Quantum Information, RWTH Aachen University — 2Institut de Physique Théorique, CEA Saclay
At zero temperature, a two-dimensional lattice of Majorana zero modes on mesoscopic superconducting islands exhibits a Z2 topologically-ordered phase, similar to the ground state of the toric code. Recently, a Landau field theory was proposed for the system that describes its phases and the different phase-transitions separating them. While the field theories for the different phase-transitions were obtained in the earlier work, the signatures of topological ordering in the different phases were not investigated in detail. This is the goal of the current work. We describe a lattice gauge theory of the Majorana toric code in terms of a U(1) matter field coupled to an emergent Z2 gauge field. Subsequently, we use a generalized Wilson-loop order-parameter, namely, the equal-time Fredenhagen-Marcu order parameter, to distinguish between the different phases. Our findings confirm the previously-obtained field theory results. In contrast to the earlier work where the topological ordering of the different phases was inferred indirectly from the Landau field theory, our method directly detects the topological ordering in the system and is thus, an independent check for the earlier results.