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arXiv · 1809.08248

Topological Mechanics from Supersymmetry

Jan Attig·Krishanu Roychowdhury·Michael J. Lawler·Simon Trebst
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Abstract

In topological mechanics, the identification of a mechanical system's rigidity matrix with an electronic tight-binding model allows to infer topological properties of the mechanical system, such as the occurrence of `floppy' boundary modes, from the associated electronic band structure. Here we introduce an approach to systematically construct topological mechanical systems by an exact supersymmetry (SUSY) that relates the bosonic (mechanical) and fermionic (e.g. electronic) degrees of freedom. As examples we discuss mechanical analogues of the Kitaev honeycomb model and of a second-order topological insulator with floppy corner modes. Our SUSY construction naturally defines hitherto unexplored topological invariants for bosonic (mechanical) systems, such as bosonic Wilson loop operators that are formulated in terms of a SUSY-related fermionic Berry curvature.

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Jan Attig, Krishanu Roychowdhury, Michael J. Lawler, Simon Trebst. 2018-09-21. Topological Mechanics from Supersymmetry. https://doi.org/10.1103/physrevresearch.1.032047

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