Multi-particle content of Majorana zero-modes in the interacting p-wave wire

Kells, G. (2015) Multi-particle content of Majorana zero-modes in the interacting p-wave wire. Physical Review B, 92 (15). ISSN 1098-0121

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In the topological phase of p-wave superconductors, zero-energy Majorana quasi-particle excitations can be well defined even in the presence of local density-density interactions. In this paper we examine this phenomenon from the perspective of matrix representations of the commutator H = [H, •] with the aim of char-acterising the multi-particle content of the many-body Majorana mode. To do this we show that, for quadratic fermionic systems, H can always be decomposed into sub-blocks that act as multi-particle generalisations of the BdG/Majorana forms that encode single-particle excitations. In this picture, density-density like interactions will break this exact excitation-number symmetry, coupling different sub-blocks and lifting degnerecies so that the eigen-operators of the commutator H take the form of individual eigenstate transitions |n)(m|. However, the Majorana mode is special in that zero-mode transitions are not destroyed by local interactions. It thus becomes possible to define our many-body Majoranas as the odd-parity zero-energy solutions of H that minimise their excitation number. This idea forms the basis for an algorithm which is used to characterise the multi-particle excitation content of the Majorana zero modes of the one-dimensional p-wave lattice model. We find that the multi-particle content of the Majorana zero-mode operators is significant even at modest interaction strengths. We will discuss how and why these findings differ from some previous work on the structure of the Majorana operators in the presence of interactions.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:30
Last Modified: 14 Dec 2022 14:10

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