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

TL;DR

This paper provides numerical evidence for the existence of a double Griffiths phase in the random quantum Ashkin-Teller chain, highlighting the complex critical behavior and phase diagram through advanced computational methods.

Contribution

It offers the first numerical confirmation of a double Griffiths phase in this model, using time-dependent DMRG and finite-size scaling analyses.

Findings

Identification of critical lines via autocorrelation peaks

Observation of maximum disorder fluctuations on critical lines

Evidence of a double Griffiths phase with diverging dynamical exponents

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.