Artificial Neural Networks as a Probe of Many-Body Localization in Novel Topologies

Beetar, Cameron

Artificial Neural Networks as a Probe of Many-Body Localization in Novel Topologies

Master Thesis

2022

Abstract

We attempt to show that artificial neural networks may be used as a tool for universal probing of many-body localization in quantum graphs. We produce an artificial neural network, training it on the entanglement spectra of the nearest-neighbour Heisenberg spin1/2 chain in the presence of extremal (definitely ergodic/localizing) disorder values and show that this artificial neural network successfully qualitatively classifies the entanglement spectra at both extremal and intermediate disorder values as being in either the ergodic regime or in the many-body-localizing regime, based on known results. To this network, we then present the entanglement spectra of systems having different topological structures for classification. The entanglement spectra of next-to-nearest-neighbour (J1 − J2, and, in particular, Majumdar-Ghosh) models, star models, and bicycle wheel models - without any further training of the artificial neural network - are classified. We find that the results of these classifications - in particular how the mobility edge is affected - are in agreement with heuristic expectations. This we use as a proof of concept that neural networks and, more generally, machine learning algorithms, endow physicists with powerful tools for the study of many-body localization and potentially other many-body physics problems.

Keywords

Applied Mathematics

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