Neural network setups for a precise detection of the many-body localization transition: Finite-size scaling and limitations

Abstract

Determining phase diagrams and phase transitions semiautomatically using machine learning has received a lot of attention recently, with results in good agreement with more conventional approaches in most cases. When it comes to more quantitative predictions, such as the identification of universality class or precise determination of critical points, the task is more challenging. As an exacting testbed, we study the Heisenberg spin-1/2 chain in a random external field that is known to display a transition from a many-body localized to a thermalizing regime, which nature is not entirely characterized. We introduce different neural network structures and dataset setups to achieve a finite-size scaling analysis with the least possible physical bias (no assumed knowledge on the phase transition and directly inputting wave-function coefficients), using state-of-the-art input data simulating chains of sizes up to L = 24. In particular, we use domain adversarial techniques to ensure that the network learns scale-invariant features. We find a variability of the output results with respect to network and training parameters, resulting in relatively large uncertainties on final estimates of critical point and correlation length exponent which tend to be larger than the values obtained from conventional approaches. We put the emphasis on interpretability throughout the paper and discuss what the network appears to learn for the various used architectures. Our findings show that a quantitative analysis of phase transitions of unknown nature remains a difficult task with neural networks when using the minimally engineered physical input.

Transition to a many-body localized regime in a two-dimensional disordered quantum dimer model

“…Our results also indicate that the machine learning analysis is also subject to finite-size effects, indicating that the use of numerical data coming from a single size may not be able to provide quantitative results for the study of phase transitions (see a discussion in Ref. [110]). One noticeable interest of the neural network analysis (already pinpointed earlier [103,105]) is that the required amount of data and overall computational cost is considerably lower than with more traditional observables to obtain approximately similar quality of prediction: For instance, good statistics on the gap ratio (Fig.…”

Distinguishing an Anderson Insulator from a Many-Body Localized phase through space-time snapshots with Neural Networks

“…Otherwise, if the accuracy is equal to one, the neural network has a perfect performance. Classifying ergodic/thermal and MBL phases with neural networks can be done with high accuracies ≈ 1 36,41,42,44 since the two phases are fundamentally distinct. However, one expects that distinguishing an MBL from the Anderson phase is a much harder problem, since the two phases are both localized and differ only in terms of the information propagation 18,66 .…”

“…Machine learning techniques have proven to be a useful tool in characterizing and understanding correlations in quantum phases of matter [25][26][27][28][29][30][31][32][33][34] . Recently, several works used machine learning to investigate the MBL transition which separates a thermal phase from the localized one [35][36][37][38][39][40][41][42][43] . In particular, in Ref.…”

Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection

“…ML has been successfully applied to a variety of physical problems, and vice versa, physics has inspired new directions to explore in understanding or improving ML techniques [1]. Among the most prominent and successful applications of ML in physics is the classification of phases in many body physics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Of particular interest are unsupervised methods that require no or little prior information for labeling [2,3,[6][7][8]21].…”