  Recent tunneling experiments on InSb hybrid superconductor-semiconductor
devices have provided hope for a stabilization of Majorana edge modes in a
spin-orbit quantum wire subject to a magnetic field and superconducting
proximity effect. Connecting the experimental scenario with a microscopic
description poses challenges of different kind, such as accounting for the
effect of interactions on the tunneling properties of the wire. We develop a
density matrix renormalization group (DMRG) analysis of the tunneling spectra
of interacting Majorana chains, which we explicate for the Kitaev chain model.
Our DMRG approach allows us to calculate the spectral function down to zero
frequency, where we analyze how the Majorana zero-bias peak is affected by
interactions. From the study of topological phase transitions between the
topological and trivial superconducting phase in the wire, we argue that the
bulk gap closure generically affects both the proximity peaks and the Majorana
peak, which should be observable in the transport signal.
