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

Abstract

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 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 $T=0,$ 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 $\ensuremath{\omega}\ensuremath{\gtrsim}T,$ 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 $\ensuremath{\omega}<T$ for the special case of spin-1/2 chains close to the planar limit (the quantum $x\ensuremath{-}y$ model) by analyzing the corresponding quantities in an equivalent model of spinless fermions with weak repulsive interactions and particle-hole symmetric disorder.