Dynamics and transport in random quantum systems governed by strong-randomness fixed points - art. no. 134424

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 momentum- and fr equency-dependent dynamic structure factor in the random singlet (RS) phase s of both spin-1/2 and spin-1 random antiferromagnetic chains, as well as i n the random dimer and Ising antiferromagnetic phases of spin-1/2 random an tiferromagnetic chains. We show that the RS phases are unusual "spin metals " with divergent low-frequency spin conductivity at T = 0, and we also foll ow the conductivity through ''metal-insulator'' transitions tuned by the st rength 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 Isin g model in the vicinity of its quantum critical point. All of the above cal culations are valid in the frequency-dominated regime omega greater than or similar toT, and rely on previously available renormalization group scheme s that describe these systems in terms of the properties of certain strong- disorder Axed-point theories. In addition, we obtain some information about the behavior of the dynamic structure factor and dynamical conductivity in the opposite "hydrodynamic" regime omega <T for the special case of spin-1 /2 chains close to the planar limit (the quantum x-y model) by analyzing th e corresponding quantities in an equivalent model of spinless fermions with weak repulsive interactions and particle-hole symmetric disorder.