Dynamics and transport in random quantum systems governed by strong-randomness fixed points

We present results on the low-frequency dynamical and transport properties of random quantum systems whose low temperature (T), low-energy behavior is controlled by strong-disorder fixed points. We obtain the momentumand frequency-dependent dynamic structure factor in the random singlet ~RS! phases of both spin-1/2 and spin-1 random antiferromagnetic chains, as well as in the random dimer and Ising antiferromagnetic phases of spin-1/2 random antiferromagnetic chains. We show that the RS phases are unusual ‘‘spin metals’’ with divergent low-frequency spin conductivity at T50, and we also follow the 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. We work out the average spin and energy autocorrelations in the one-dimensional random transverse-field Ising model in the vicinity of its quantum critical point. All of the above calculations are valid in the frequency-dominated regime v*T , and rely on previously available renormalization group schemes that describe these systems in terms of the properties of certain strong-disorder fixed-point theories. In addition, we obtain some information about the behavior of the dynamic structure factor and dynamical conductivity in the opposite ‘‘hydrodynamic’’ regime v,T for the special case of spin-1/2 chains close to the planar limit ~the quantum x-y model! by analyzing the corresponding quantities in an equivalent model of spinless fermions with weak repulsive interactions and particle-hole symmetric disorder.