Hom-Lie-Virasoro symmetries in Bloch electron systems and quantum plane in tight binding models
arXiv:2303.17347 · doi:10.1016/j.nuclphysb.2023.116336
Abstract
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 translational groups, which determine phase factors for a -bracket commutator. The phase factors can be formulated as a -ordered product of the commutable operators by interpreting the AB phase factor of discrete MT action as fluctuation parameter of a quantum plane. We also show that some sequences of TBM Hamiltonians are described by the CZ generators.
arXiv comment35 pages, 2 figures, Errors are corrected (minor revision)
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