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Using the density-matrix renormalization group, we determine the differenttopological phases and low-energy excitations of a time-reversal invarianttopological superconducting (TRITOPS) wire with extended s-wavesuperconductivity, Rashba spin-orbit coupling (SOC) and on-site repulsion $U$,under an externally applied Zeeman field $J$. For the case in which $J$ isperpendicular to the SOC, the model describes a chain of Shiba impurities ontop of a superconductor with extended superconductor pairing. We identify thedifferent topological phases of the model at temperature $T=0$, and inparticular study the stability of the TRITOPS phase against the Zeeman field$J$ and the chemical potential $\mu$, for different values of $U$. In the casewhere the magnetic field $J$ is perpendicular to the SOC axis, the pair ofKramers-degenerate Majorana zero modes at the edges of the system that existfor $J=0$, remain degenerate until a critical value of the magnetic field isreached. For $J$ parallel to the SOC and up to moderate values of $U$, thefractional spin projection $\langle S_y \rangle=1/4$ at the ends, found fornon-interacting wires at $U=0$, is recovered. In addition, the analyticexpression that relates $\langle S_y \rangle$ with $J$ for finitenon-interacting chains is shown to be universal up to moderate values of $U$.

Topological phases of strongly-interacting time-reversal invariant topological superconducting chains under a magnetic field