  We study the fidelity decay in the $k$-body embedded ensembles of random
matrices for bosons distributed in two single-particle states, considering the
reference or unperturbed Hamiltonian as the one-body terms and the diagonal
part of the $k$-body embedded ensemble of random matrices, and the perturbation
as the residual off-diagonal part of the interaction. We calculate the
ensemble-averaged fidelity with respect to an initial random state within
linear response theory to second order on the perturbation strength, and
demonstrate that it displays the freeze of the fidelity. During the freeze, the
average fidelity exhibits periodic revivals at integer values of the Heisenberg
time $t_H$. By selecting specific $k$-body terms of the residual interaction,
we find that the periodicity of the revivals during the freeze of fidelity is
an integer fraction of $t_H$, thus relating the period of the revivals with the
range of the interaction $k$ of the perturbing terms. Numerical calculations
confirm the analytical results.
