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Zeitschrift für Physik B Condensed Matter

Exactly solvable 1D frustrated quantum spin models

Д. В. Дмитриев, V. Ya. Krivnov, А. А. Овчинников

Published Jun 1, 1996• 9 citations
Publisher
DOI
10.1007/s002570050358

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We present a graph-theoretic characterization of when a quantum spin model admits an exact solution via a mapping to free parafermions. Our characterization 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. Furthermore, 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 characterization extends that given for free-fermion solvability. Finally, we apply our results to solve three qudit spin models.