Data and data processing tools supporting results presented in publication "Exact zero modes in interacting Majorana X- and Y-junctions"

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This dataset includes data obtained from exact diagonalizations of an Hamiltonian describing a system of interacting Majorana chains (the Kitaev chain) coupled in junctions. We do this to report the report the emergence of exact zero modes in junctions of two, three and four short interacting Majorana wires, equivalent to a chain with an impurity bond, Y- and X- junctions respectively. These exact zero modes arise from incommensurate short-range correlations induced by interacting Majorana fermions and manifest as exact level crossings between in-gap states upon continuously tuning the interaction strength. In a junction of only two chains we report exact zero modes and parity switching as soon as the coupling between the chains across a junction is positive. Remarkably, for junctions with multiple chains the in-gap states group up into sets of parity pairs -- pairs of states with opposite parity and similar energies. We demonstrate that the formation of these parity pairs are always due to the effective interaction of the outer edges of the junction. The behavior within each pair can be efficiently described by two coupled chains. In the Y-junction, we detect four in-gap states …

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