Abstract
We study the level spacing distributions across the many-body localization (MBL) transition in random spin systems, and compare them to the short-range plasma model (SRPM) with interaction range k and inverse temperature β. It is found the level statistics within the ergodic phase fits well into SRPM, with the interaction range k decreases as randomness strength grows. Particularly, SRPM with only nearest level interactions (k=1) fits well with the physical data at the ergodic-MBL transition point identified by the inter-sample randomness, suggesting the former is the effective critical model with β=1(2) for time-reversal invariant (broken) systems.
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