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arXiv · 2610.20166

Quantized six-vertex realizations of frustration graphs

Atsuo Kuniba·Souta Oikawa
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Abstract

A recent graph-theoretic criterion for a Hamiltonian to exhibit a free-parafermion spectrum is that its frustration graph be an indifference graph. We show that an arbitrary finite indifference graph can be realized as a frustration graph of the quantized six-vertex model at odd roots of unity, by a suitable choice of the defining wiring diagram and parameters. This provides a concrete realization of the criterion through the quantum Frobenius property of the quantized six-vertex model, recently established from its three-dimensional integrable structure.

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Atsuo Kuniba, Souta Oikawa. 2026-10-14. Quantized six-vertex realizations of frustration graphs. https://arxiv.org/abs/2610.20166

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