Abstract. The random quantum Ashkin-Teller chain is studied numerically by means of time-dependent Density-Matrix Renormalization Group. The critical lines are estimated as the location of the peaks of the integrated autocorrelation times, computed from spin-spin and polarization-polarization autocorrelation functions. Disorder fluctuations of magnetization and polarization are observed to be maximum on these critical lines. Entanglement entropy leads to the same phase diagram, though with larger finite-size effects. The decay of spin-spin and polarization-polarization autocorrelation functions provides numerical evidence of the existence of a double Griffiths phase when taking into account finite-size effects. The two associated dynamical exponents z increase rapidly as the critical lines are approached, in agreement with the recent conjecture of a divergence at the two transitions in the thermodynamic limit. PACS

Recently has been investigated that the ground-state wavefunction of the one dimensional quantum spin-1/2 chain models is multifractal in general with nontrivial fractal dimension. We are studying this phenomena for the quantum Ising chain with aperiodic perturbation. By performing a block real-space renormalization approach, we obtain the ground-state wave function and we extract the generalized multifractal dimension and the multifractal spectrum. For a spin chain with negative wandering exponent the multifractal quantities have the same behavior with the unperturbed chain while for a spin chain with a vanishing wandering exponent are dependent on the coupling ratio. Finally, for a spin chain with positive wandering exponent, the multifractal quantities present a different non-linear behavior. arXiv:1910.05931v1 [cond-mat.dis-nn]