TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.7.1.001
TI  - Quantum walks on graphs of the ordered Hamming scheme and spin networks
PY  - 2019/07/02
UR  - https://scipost.org/SciPostPhys.7.1.001
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 7
IS  - 1
SP  - 001
A1  - Miki, Hiroshi
AU  - Tsujimoto, Satoshi
AU  - Vinet, Luc
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.7.1.001,
	title={{Quantum walks on graphs of the ordered Hamming scheme and spin networks}},
	author={Hiroshi Miki and Satoshi Tsujimoto and Luc Vinet},
	journal={SciPost Phys.},
	volume={7},
	pages={001},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.7.1.001},
	url={https://scipost.org/10.21468/SciPostPhys.7.1.001},
}