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arXiv · 2408.09684

A Graph-Theoretic Framework for Free-Parafermion Solvability

Ryan L. Mann·Samuel J. Elman·David R. Wood·Adrian Chapman
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Abstract

We present a graph-theoretic characterisation of when a quantum spin model admits an exact solution via a mapping to free parafermions. Our characterisation is based on the concept of a frustration graph, which represents the commutation relations between Weyl operators of a Hamiltonian. We show that a quantum spin system has an exact free-parafermion solution if its frustration graph is an oriented indifference graph. Further, we show that if the frustration graph of a model can be dipath oriented via switching operations, then the model is integrable in the sense that there is a family of commuting independent set charges. Additionally, we establish an efficient algorithm for deciding whether this is possible. Our characterisation extends that given for free-fermion solvability. Finally, we apply our results to solve three qudit spin models.

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Ryan L. Mann, Samuel J. Elman, David R. Wood, Adrian Chapman. 2024-08-19. A Graph-Theoretic Framework for Free-Parafermion Solvability. https://doi.org/10.1098/rspa.2024.0671

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