Majorana edge modes in number-conserving models with long-range interactions

Topological superconductors are believed to host exotic quasiparticle excitations known as Majo-

rana zero-modes, with much of the evidence based on BCS mean-field theory. The direct application

of mean-field arguments is tenuous in finite, isolated systems relevant in some experiments. Here,

we numerically study fermion number-conserving models with long-range interactions, which un-

der periodic boundary conditions exhibit robust topological and non-topological superconductivity,

tuned by the strength of interaction [1]. We find evidence that, on the topological side, Majorana

edge modes appear in open chains, manifesting as the vanishing of the energy splitting between

odd- and even-parity ground states with increasing system size. Additionally, off-diagonal two-

point correlation functions show nonlocal, parity-dependent edge effects consistent with Majorana

phenomenology. We develop a correlation-based method revealing the spatial structure of Majorana

modes in this fully interacting many-body setting.