We numerically investigate Heisenberg XXZ spin-1/2 chain in a spatially random (disordered) static magnetic field. We find that time dependent density matrix renomalization group simulations of time evolution of the model can be performed efficiently. Namely, the dimension of matrices needed to efficiently represent the time-evolution increases linearly with time, or entanglement entropy of typical bipartition of the lattice grows logarithmically in time. This has to be contrasted with exponential inefficiency of classical simulations of non-integrable spin chains in homogeneous fields.

As a result, we have shown that infinite temperature spin-spin correlation function of XXZ model in the random field displays exponential localization in space indicating insulating behaviour, or absence of spin diffusion. Similar results have been found for other examples of non-integrable spin chains with nearest neighbour interaction in external random fields.