Numerical evidence of the double-Griffiths phase of the random quantum Ashkin-Teller chain
Groupe de Physique Statistique, Département P2M, Institut Jean Lamour (CNRS UMR 7198), Université de Lorraine, 54500 Vandoeuvre les Nancy, France
Received: 22 July 2015
Received in final form: 21 November 2015
Published online: 25 January 2016
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2016