A Graph-Theoretic Framework for Free-Parafermion Solvability

• URL: http://arxiv.org/abs/2408.09684v1
• Date: Mon, 19 Aug 2024 03:43:43 GMT
• Title: A Graph-Theoretic Framework for Free-Parafermion Solvability
• Authors: Ryan L. Mann, Samuel J. Elman, David R. Wood, Adrian Chapman,
• Abstract summary: We show that a quantum spin system has an exact free-parafermion solution if its frustration graph is an oriented indifference graph. We also 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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