Detection of Berezinskii-Kosterlitz-Thouless transition via Generative Adversarial Networks

Abstract

The detection of phase transitions in quantum many-body systems with lowest possible prior knowledge of their details is among the most rousing goals of the flourishing application of machine-learning techniques to physical questions. Here, we train a Generative Adversarial Network (GAN) with the Entanglement Spectrum of a system bipartition, as extracted by means of Matrix Product States ansätze. We are able to identify gapless-to-gapped phase transitions in different one-dimensional models by looking at the machine inability to reconstruct outsider data with respect to the training set. We foresee that GAN-based methods will become instrumental in anomaly detection schemes applied to the determination of phase-diagrams.

Fluctuation based interpretable analysis scheme for quantum many-body snapshots

“…As a concrete example, deep neural networks have been increasingly utilized to predict phase transitions in physical systems, the model's input data types ranging from entanglement entropy spectra [1,[20][21][22] to quantum image data generated numerically [23][24][25][26][27][28] and experimentally [29][30][31][32]. However, one major drawback of the neural network toolbox is their inherent black-box nature, which limits interpretation -and in turn restricts their applicability towards developing microscopic theories of yet unsolved physical regimes.…”

Phase Diagram Detection via Gaussian Fitting of Number Probability Distribution

“…Its structures embed information about non-local quantum correlations, as formalized within the bulk-boundary correspondence framework [9][10][11]. Both ad-hoc defined order parameters [12,13] and machine learning driven approaches [14][15][16] have been employed for the detection of phase transitions. Last, but certainly not least, the evolution of entanglement properties under the system dynamics has recently unveiled the existence of new kinds of non-equilibrium phase transitions for quantum many-body systems under random projective measurements or unitary gates [17][18][19].…”