Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain

Christophe Chatelain (1) , Dimitrios Voliotis (1)

1 IJL - Institut Jean Lamour

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.

Mots clés: 0530Rt; 0570Jk; 0510-a

Domaines: Mécanique statistique [cond-mat.stat-mech]

Christophe Chatelain, Dimitrios Voliotis. Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain. The European Physical Journal B: Condensed Matter and Complex Systems, 2016, 89, pp.18. ⟨10.1140/epjb/e2015-60593-3⟩. ⟨hal-01158447v2⟩