Exploring many-body localization and thermalization using semiclassical methods

“…CTWA works well both at low disorder and at high disorder, but it clearly fails to reproduce localization at intermediate values of disorder. This is consistent with earlier work 20,21 observing that classical disordered spin chains in thermodynamic limit eventually show ergodic diffusive behavior. Our numerical results (bottom plots) indeed indicate that irrespective of the cluster size long time dynamics with CTWA approximation is always diffusive.…”

“…The agreement shown here suggests that in the longtime limit GDTWA simulations for simple single-spin observables approach the results expected from closed system quantum thermalization, an effect also observed previously for different initial states for S = 1/2 [48] and S = 3 [29] models. Note that while our simulations do not constitute a general proof of thermalization in the GDTWA, our results here suggest that in models which feature quantum thermalization, i.e.…”

“…The different steady-state behavior seen in integer and half-integer spin systems is reminiscent of their different low energy spectra at equilibrium. The agreement shown here suggests that in the long-time limit GDTWA simulations for simple single-spin observables approach the results expected from closed system quantum thermalization, an effect also observed previously for different initial states for = S 1 2 [48] and S=3 [29] models. Note that while our simulations do not constitute a general proof of thermalization in the GDTWA, our results here suggest that in models which feature quantum thermalization, i.e.in models which are not many-body localized, and with local observables that thermalize quickly, the GDTWA can give accurate predictions for simple observables not only at short times, but over all relevant timescales.…”

“…It means that fTWA gives the best prediction of quantum dynamics for weak and strong tilts. Such a feature was previously also observed for disordered systems when the disorder strength was varied [37,63]. Moreover, we also noticed that in the (iii) regime and charge channel, fTWA imbalances decay faster than the corresponding ones in ED, which suggests that fTWA dynamics can be regarded as an upper bound for relaxation rates.…”