A Graph-Theoretic Framework for Free-Parafermion Solvability
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908335334227968 |
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| author | Mann, Ryan L. Elman, Samuel J. Wood, David R. Chapman, Adrian |
| author_facet | Mann, Ryan L. Elman, Samuel J. Wood, David R. Chapman, Adrian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09684 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Graph-Theoretic Framework for Free-Parafermion Solvability Mann, Ryan L. Elman, Samuel J. Wood, David R. Chapman, Adrian Quantum Physics Statistical Mechanics Strongly Correlated Electrons Combinatorics 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. |
| title | A Graph-Theoretic Framework for Free-Parafermion Solvability |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons Combinatorics |
| url | https://arxiv.org/abs/2408.09684 |