Topological phase transitions of interacting Majorana fermions in an array of vortices

We study a vortex array in a p-wave superconducting thin film that produces ladder-like lattices with interacting Majorana fermions. We construct a model Hamiltonian with parameters which are tunable via the deformation of the vortex array. We explore topological phase transitions of the system and compute phase diagrams using the density-matrix-renormalization-group method. We further investigate transport properties for experimental detection. Our results have potential application on building devices to engineer strongly correlated Majorana fermions.