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arXiv · 2509.00158

Majorana edge modes in isolated wires

Jaden Thomas-Markarian·Kartiek Agarwal·Ivar Martin
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Abstract

Topological superconductors are believed to host exotic quasiparticle excitations known as Majorana zero-modes (MZMs), 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 develop a new correlation-based method for identifying MZMs in interacting, number-conserving systems. Using DMRG, we study fermion number-conserving models with long-range interactions, which under 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. These correlations reveal the spatial structure of Majorana modes in the many-body wavefunction. We show that the correlation diagnostic applies broadly, including to short-range interacting models, where topological superconductivity is more fragile due to the absence of a bulk excitation gap.

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Jaden Thomas-Markarian, Kartiek Agarwal, Ivar Martin. 2025-08-29. Majorana edge modes in isolated wires. https://doi.org/10.1103/97fb-45n9

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