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Journal of Physics A Mathematical and General

Supersymmetry and spin systems

Hermann Nicolai

Published Sep 1, 1976• 199 citations
Publisher

Abstract

It is shown that supersymmetry may be applied to spin systems. A simple algebra is proposed and various examples are discussed. It is argued that certain correlation functions must vanish on account of supersymmetry.
DOI
10.1088/0305-4470/9/9/010

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The interplay between supersymmetry and classical and quantum computation is discussed. First, it is shown that the problem of computing the Witten index of N≤2\mathcal N \leq 2N≤2 quantum mechanical systems is #P\#P#P-complete and therefore intractable. Then, the notions of supersymmetry in the space of qubits and supersymmetric quantum circuits are introduced and some of their properties discussed. In particular, it is shown that these define a nontrivial subclass of quantum algorithms with robustness properties typical of supersymmetric systems. Concrete examples, including the supersymmetric SYK model and fermion hard-core models are discussed. Some applications and open questions are suggested.
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