Signatures of Majorana zero modes in an isolated one-dimensional superconductor

Abstract

We examine properties of the mean-field wave function of the one-dimensional Kitaev model supporting Majorana zero modes (MZMs) when restricted to a fixed number of particles. Such wave functions can, in fact, be realized as exact ground states of interacting number-conserving Hamiltonians and amount to a more realistic description of the finite isolated superconductors. Akin to their mean-field parent, the fixed-number wave functions encode a single electron spectral function at zero energy that decays exponentially away from the edges, with a localization length that agrees with the mean-field value. Based purely on the structure of the number-projected ground states, we construct the fixed particle number generalization of the MZM operators. They can be used to compute the edge tunneling conductance; however, notably the value of the zero-bias conductance remains the same as in the mean-field case, quantized to 2e2/h. We also compute the topological entanglement entropy for the number-projected wave functions and find that it contains a robust ln(2) component as well as a logarithmic correction to the mean-field result, which depends on the precise partitioning used to compute it. The presence of the logarithmic term in the entanglement entropy indicates the absence of a spectral gap above the ground state; as one introduces fluctuations in the number of particles, the correction vanishes smoothly.

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