It is shown that the hopping of a single excitation on certain triangular spin lattices with non-uniform couplings and local magnetic fields can be described as the projections of quantum walks on graphs of the ordered Hamming scheme of depth 2. For some values of the parameters the models exhibit perfect state transfer between two summits of the lattice. Fractional revival is also observed in some instances. The bivariate Krawtchouk polynomials of the Tratnik type that form the eigenvalue matrices of the ordered Hamming scheme of depth 2 give the overlaps between the energy eigenstates and the occupational basis vectors.
Cited by 3
Miki et al., Classical and quantum walks on paths associated with exceptional Krawtchouk polynomials
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Bernard et al., Entanglement of inhomogeneous free fermions on hyperplane lattices
Nuclear Physics B 984, 115975 115975 (2022) [Crossref]
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- 1 Meteorological College
- 2 京都大学 / Kyoto University
- 3 Université de Montréal / University of Montreal