1. A Graph-Theoretic Framework for Free-Parafermion Solvability
- Author
-
Mann, Ryan L., Elman, Samuel J., Wood, David R., and Chapman, Adrian
- Subjects
Quantum Physics ,Condensed Matter - Statistical Mechanics ,Condensed Matter - Strongly Correlated Electrons ,Mathematics - Combinatorics - 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., Comment: 22 pages, 2 figures
- Published
- 2024