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Quantized six-vertex realizations of frustration graphs
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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BibTeX
@misc{kuniba2026quantized,
title = {{Quantized six-vertex realizations of frustration graphs}},
author = {Atsuo Kuniba and Souta Oikawa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20166},
eprint = {2610.20166},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20166},
}
RIS
TY - UNPB
TI - Quantized six-vertex realizations of frustration graphs
AU - Atsuo Kuniba
AU - Souta Oikawa
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20166
UR - https://arxiv.org/abs/2610.20166
AB - 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.
ER -