Analysis of many-body localization transitions in Floquet systems: Random versus quasi-periodic disorder

We investigate many-body localization (MBL) phase transitions in Floquet-driven quantum systems, employing global quantum discord (GQD) to compare the stability and dynamics of MBL phases under random and quasi-periodic disorder. For a static Heisenberg spin-$1/2$ ladder, GQD reveals critical disorder strengths of $W_c\approx 9.5$ (random case) and $W_c\approx 8.5$ (quasi-periodic case), highlighting the greater stability of quasi-periodic disorder. In Floquet systems, high-frequency drives ($\omega >20$) suppress energy absorption, preserving MBL even in weakly disordered ergodic regimes, while low frequencies ($\omega <2$) or strong amplitudes promote thermalization. Quasi-periodic disorder exhibits superior resistance to thermalization, with higher critical driving amplitudes, attributed to robust internal correlations quantified by GQD. Variance analysis confirms the consistency of these critical points. Our findings clarify the distinct stabilization mechanisms of driving parameters in Floquet-MBL systems, while demonstrating quasi-periodic disorder’s inherent robustness against perturbations, offering guidance for the experimental realization of nonergodic quantum states.