One-excitation spin dynamics in homogeneous closed chain governed by XX-Hamiltonian

We analytically investigate the one-excitation spin dynamics in a homogeneous closed spin-1/2 chain via diagonalization of the one-excitation block of the XX-Hamiltonian, which allows to derive the analytical expressions for probability amplitudes describing state transfers between any two spins of a chain. We analytically investigate the M-neighbor approximation ( \(M\ge 1\) $M\ge 1$ ) of spin dynamics with arbitrary initial state and analyze its accuracy using special integral characteristics defined in terms of the above probability amplitudes. We find M providing the required accuracy of evolution approximation for chains of different lengths.