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A new solvable 3-dimensional spin lattice Hamiltonian with inhomogeneous couplings, which can be diagonalized by 3-variable Krawtchouk polynomials, is proposed. The model is defined on the lattice of rectangular pyramid and describes near-neighbor interactions instead of nearest-neighbor ones. Using the properties of 3-variable Krawtchouk polynomials, quantum state transfer in the model is analyzed. In particular, for some value of the parameters, perfect state transfer is shown to occur from the apex to the diagonal plane.

3-dimensional solvable XX spin lattice Hamiltonian derived from 3-variable Krawtchouk polynomials