Hom-Lie-Virasoro symmetries in Bloch electron systems and quantum plane in tight binding models
| Autor: | Aizawa, Naruhiko, Sato, Haru-Tada |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Nucl, Phys. B995 (2023) 116336 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.nuclphysb.2023.116336 |
| Popis: | We discuss the Curtright-Zachos (CZ) deformation of the Virasoro algebra and its extentions in terms of magnetic translation (MT) group in a discrete Bloch electron system, so-called the tight binding model (TBM), as well as in its continuous system. We verify that the CZ generators are essentially composed of a specific combination of MT operators representing deformed and undeformed $U(1)$ translational groups, which determine phase factors for a $\ast$-bracket commutator. The phase factors can be formulated as a $\ast$-ordered product of the commutable $U(1)$ operators by interpreting the AB phase factor of discrete MT action as fluctuation parameter $q$ of a quantum plane. We also show that some sequences of TBM Hamiltonians are described by the CZ generators. Comment: 35 pages, 2 figures, Errors are corrected (minor revision) |
| Databáze: | arXiv |
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