[en] We study the critical level statistics at the many-body localization (MBL) transition region in random spin systems. By employing the inter-sample randomness as indicator, we manage to locate the MBL transition point in both orthogonal and unitary models. We further count the nth order gap ratio distributions at the transition region up to n = 4, and find they fit well with the short-range plasma model with inverse temperature β = 1 for orthogonal model and β = 2 for unitary. These critical level statistics are argued to be universal by comparing results from systems both with and without total S _z conservation. We also point out that these critical distributions can emerge from the spectrum of a Poisson ensemble, which indicates the thermal-MBL transition point is more affected by the MBL phase rather than thermal phase. (paper)

[en] We employ the methods of machine learning to study the many-body localization (MBL) transition in a 1D random spin system. By using the raw energy spectrum without pre-processing as training data, it is shown that the MBL transition point is correctly predicted by the machine. The structure of the neural network reveals the nature of this dynamical phase transition that involves all energy levels, while the bandwidth of the spectrum and nearest level spacing are the two dominant patterns and the latter stands out to classify phases. We further use a comparative unsupervised learning method, i.e., principal component analysis, to confirm these results. (paper)

[en] The transition between thermal and many-body localized phases in isolated random spin systems are typically identified by the distribution of nearest level spacings. In this work, by employing machine learning methodology, we show this transition can be learnt through raw energy spectrum without any pre-processing. After achieving so in conventional random spin chain with differentiable level spacing distributions, we further construct novel models with misleading signatures of level spacing, and show machine can defeat the latter when training data is raw energy spectrum. Our work shows the low-level energy spectrum contains more information than level spacings, and can be captured by machine in a direct while efficient way, which makes it a promising new tool for studying a variety of isolated quantum systems. (paper)

[en] Highlights: • The higher-order level spacing distributions along the MBL transition are fitted to the short-range plasma model (SRPM). • The SRPM reproduces the level statistics with high accuracy for the whole ergodic phase. • The effective model for the MBL transition point is verified to be SRPM with only nearest neighboring interactions. 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 $\beta =1(2)$ for time-reversal invariant (broken) systems.

[en] We employ a convolutional neural network to explore the distinct phases in random spin systems with the aim to understand the specific features that the neural network chooses to identify the phases. With the energy spectrum normalized to the bandwidth as the input data, we demonstrate that a network of the smallest nontrivial kernel width selects level spacing as the signature to distinguish the many-body localized phase from the thermal phase. We also study the performance of the neural network with an increased kernel width, based on which we find an alternative diagnostic to detect phases from the raw energy spectrum of such a disordered interacting system. (paper)