Dynamics and transport in random antiferromagnetic spin chains

We present the first results on the low-frequency dynamical and transport properties of random antiferromagnetic spin chains at low temperature (T). We obtain the momentum and frequency dependent dynamic structure factor in the random singlet (RS) phases of both spin-1/2 and spin-1 chains, as well as in the random dimer phase of spin-1/2 chains. We also show that the RS phases are unusual "spin-metals" with divergent low-frequency conductivity at T = 0, and follow the spin conductivity through "metal-insulator" transitions tuned by the strength of dimerization or Ising anisotropy in the spin-1/2 case and by the strength of disorder in the spin-1 case.