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Keywords = quadratic fermionic models

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18 pages, 329 KB  
Article
A Z3-Graded Lie Superalgebra with Cubic Vacuum Triality
by Yuxuan Zhang, Weitong Hu and Wei Zhang
Symmetry 2026, 18(1), 54; https://doi.org/10.3390/sym18010054 - 27 Dec 2025
Viewed by 2044
Abstract
We construct a finite-dimensional Z3-graded Lie superalgebra of dimensions (12,4,3), featuring a grade-2 sector that obeys a cubic bracket relation with the fermionic sector. This induces an emergent triality symmetry cycling the three components. The full set of graded Jacobi identities [...] Read more.
We construct a finite-dimensional Z3-graded Lie superalgebra of dimensions (12,4,3), featuring a grade-2 sector that obeys a cubic bracket relation with the fermionic sector. This induces an emergent triality symmetry cycling the three components. The full set of graded Jacobi identities is verified analytically in low dimensions and numerically in a faithful 19-dimensional matrix representation, with residuals 8×1013 over 107 random tests. Explicit quadratic and cubic Casimir operators are computed, with proofs of centrality, and the adjoint representation is shown to be anomaly-free. The algebra provides a minimal, closed extension beyond conventional Z2 supersymmetry and may offer an algebraic laboratory for models with ternary symmetries. Full article
(This article belongs to the Special Issue Symmetry and Lie Algebras)
20 pages, 1502 KB  
Article
Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models
by Miroslav Hopjan and Lev Vidmar
Entropy 2024, 26(8), 656; https://doi.org/10.3390/e26080656 - 31 Jul 2024
Cited by 1 | Viewed by 2009
Abstract
We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in the site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of single-particle states. We then generalize our statement to [...] Read more.
We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in the site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of single-particle states. We then generalize our statement to a similar relationship between the non-equal time and space density correlation functions in many-body states, and the transition probabilities of single-particle states at nonzero distances. Finally, we study the equal-time connected density–density correlation functions in many-body states, which exhibit certain qualitative analogies with the survival and transition probabilities of single-particle states. Our results are numerically tested for two paradigmatic models of single-particle localization: the 3D Anderson model and the 1D Aubry–André model. This work gives an affirmative answer to the question of whether it is possible to measure features of single-particle survival and transition probabilities by the dynamics of observables in many-body states. Full article
(This article belongs to the Section Statistical Physics)
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